“Nice place!” the actor Bryan Cranston said to President Obama as he glanced around at the White House. “When are you putting it on the market?”

The Oval Office looks eerily familiar, even to a couple of first-time visitors: that solid oak desk with the South Lawn behind it through floor-to-ceiling windows; the pair of comfortable-looking sofas on an oval rug with the presidential seal; and on a gray afternoon, a nimbus of light glowing above the crown molding at the ceiling.

“I’m only leasing,” Mr. Obama replied. “I just want to make sure I get my security deposit back.”

The president showed us around the Oval Office and its adjoining private dining room, chatting about items of particular significance to him: a handwritten draft of a speech by President Kennedy; a seascape painted by Senator Edward M. Kennedy, who gave it to Mr. Obama when he was a senator; and, next to three family photos, a pair of red boxing gloves signed “To Barack” by Muhammad Ali.

For Mr. Cranston, who won four Emmys for his role in “Breaking Bad,” a show that Mr. Obama has said that he, like millions of Americans, binge-watched, this visit had the feeling of déjà vu.

“I’ve been in a replica of this room so much I feel like I’ve been here,” he said, referring to the set of “All the Way,” an HBO film premiering on May 21 about the first year in the presidency of Lyndon B. Johnson, during which he fought to pass the Civil Rights Act of 1964. (Mr. Cranston, 60, won a Tony Award in 2014 for his performance in “All the Way” on Broadway.) The aptness of this pairing did not escape Mr. Obama, who said he credited President Johnson’s civil rights laws for “ultimately leading to the election of representatives who look like me.”

But unlike the president in Mr. Cranston’s film, who has just ascended to the position after the assassination of President Kennedy and is only beginning to make his mark on the office, Mr. Obama, 54, is in the homestretch of his second term and clearly thinking about his legacy. This interview took place on April 29; the next night, the president would give his final address at the annual White House Correspondents’ Association dinner (which Mr. Cranston attended), ending his speech with the words “Obama out” and a dramatic mic drop.

Mr. Obama invited us to take off our jackets and get comfortable; he was already in shirt sleeves. He offered cookies and drinks, or to “whip something up.” And for the next hour, the pair spoke not only of how politics (and the country) have changed since the days of Mr. Johnson’s Great Society, but also about the tonic of solid family lives after turbulent youths, the generational shift ushered in by the Obama presidency and how the digital age has made this president, in his words, “probably the most recorded, filmed and photographed person in history.”

Philip Galanes: Mr. President, I have to tell you: Right now I’m sweating. Does it bum you out to be the guy who stresses out most people he meets?

Barack Obama: Actually, I’m very easygoing. The office is stressful for people. When you work here, you lose that sense of awe on a day-to-day basis, but you recover it through somebody else’s eyes — through visitors or friends who come for the first time. But if I’m walking home late at night, down the Colonnade, there’s a majesty you never lose. This is the same walk Kennedy took, that F.D.R. wheeled himself down.

PG: Is it a nice change, Bryan, being the second-most-famous person in the room?

Bryan Cranston: I love it! When I set out to be an actor, I just wanted to tell stories. The fact that great fortune came and allowed me to become famous is almost a distraction from what I wanted to do. When I meet people now, they only want to talk about me. I get bored with that. I want to find out what you’re doing, but the dynamic shifts the other way.

BO: It’s one of the downsides of any celebrity. People have an idea of who you are. So some of the spontaneity you had before, making change in a coffee shop or striking up a conversation, disappears. But those moments are precious, and the loss of anonymity turns out to be more profound than you realized. The saving grace for Michelle and me is that we didn’t become famous until later in life. I wasn’t a national figure until I was 43. I had a full life of wheeling the grocery cart with my daughter in the front.

BC: And that probably gave you more maturity to handle the experience.

BO: I remember the day after I gave my speech at the [2004 Democratic] convention in Boston, the one that catapulted me to national prominence. I was talking to a friend who was reacting to the craziness, and I said, “I’m no smarter today than I was two days ago.” It makes you wonder about kids — 16, 17, 20 — whether they’re actors or sports stars, who suddenly have to deal with this. Now, these are high-class problems, and I’m always careful to say that being able to do what you love is an incredible privilege.

BC: How did you feel about your girls being put in that position?

BO: It was probably our biggest worry before we came here. And it’s testimony entirely to Michelle and my mother-in-law [Marian Robinson, who moved into the White House with the Obama family in 2008] that they’ve turned out to be such terrific grounded kids. I give credit to the press for sticking with an unspoken rule not to follow them around and give them space to grow. They’re pretty much able to do anything their friends do. In some ways, it was part of our decision for me to run when I did because we thought it would be easier for them when they were younger. It would be a great challenge to land here as a teenager under a spotlight.

PG: This reminds me of your after-school life as a kid: cartoons and sitcom reruns, homework before dinner, then fighting for the TV remote all night. The president was just like me and every kid I knew — the first to have that wall-to-wall engagement with pop culture.

BO: That’s interesting.

BC: Sounds familiar to me, too. But I had a challenging childhood that was touched by alcoholism and a need to grow up quicker than most kids do.

PG: Which brings me to an interesting commonality: All three of us grew up without fathers. Mine drifted into depression and suicide. Bryan’s was absent for 10 years — between 10 and 21, and the president met his dad just once at 10 or 11. Were you looking for dads everywhere, like me?

BC: Not consciously. When you’re a kid, you deal with circumstances the way they are. I did want to be a policeman, early on. That’s a very masculine role model, and I followed that path for a while. I had an aptitude for it. But as every young man should, I decided to go into acting because the girls were much prettier in acting class. But I’ve come to see that parents are always teaching you. In the best case, it’s how to behave. What I try to do in my life now is show our daughter a loving relationship with her mother. But sometimes, and largely with my parents, they teach you what not to do: “I’m not going down that road; it’s a dead end.” So I veered off in other directions and, of course, made mistakes going that way as well.

BO: There’s a wonderful quote that I thought was L.B.J.’s, but I could never verify it: “Every man is either trying to live up to his father’s expectations or make up for his father’s mistakes.” I spent a lot of time trying to figure out, in the absence of an immediate role model, what it meant to be a man — or in my case, a black man or a man of mixed race in this society. But as Bryan said, there’s no checklist. It’s only later you realize the things you may have done in search of that absent father.

PG: I bet it’s had a big effect on how you both raised your daughters.

BO: There was a powerful sense that I wanted to get this right. Not that I was going to be perfect, but that I was going to be there, and engage, and try to figure this out. Now I had the benefit of a great relationship with my mom, and she taught me the essential elements of parenting: unconditional love and explaining your values to your kids, having high expectations. And Michelle comes from a very close family.

BC: As did my wife.

BO: I always think part of the attraction for me, other than her great legs and being smart as a whip, was the stability she had with her tight-knit family. Being grounded and in one place for her entire childhood. And I think part of the attraction for her was that I was this exotic guy, who had done a whole bunch of stuff.

BC: My wife, Robin, was from a stable family, too. There was something so attractive about that. I thought, “This is what I want.” It’s still choppy waters raising kids, but I could never conceive of not being there.

PG: There’s a beautiful moment in your L.B.J. movie, where you come out of the Oval Office and bump into your daughter. You have this wistful look in your eyes, like, “Have I sacrificed my relationship with this girl to this office?”

BC: I pitched that scene. It wasn’t in the play. I wanted you to feel the father’s love and his sense of regret that even though he’s so busy with the world’s problems ——

BO: He’s still longing to connect.

PG: Both of you must feel that, with your grinding schedules.

BO: How old is your daughter?

BC: She’s 23.

BO: So, you’re a little ahead of me. Malia, my oldest, is about to leave for college. [The White House announced this week that Malia Obama was accepted at Harvard and that she intends to start in the fall of 2017, after taking a gap year.] So this stirs up all kinds of strong feelings. But ironically, being in the White House gave me more time with the girls because ——

BC: The commute was so short.

BO: I live above the store. We’ve been able to schedule, pretty religiously, dinner at 6:30 every night for the last eight years. If I had a trip, I might be gone for a few days. But as busy as I was, I was able to go upstairs, have dinner. They don’t want you for more than an hour once they hit teenage. Then I can always come back down here and work. It was a great and unexpected prize of this office. But you do think about it as your daughter is about to leave: What did I miss? The one thing I never lost, in a way that somebody like L.B.J. might have — who was hungry for the office in a way that I wasn’t — is my confidence that, with my last breath, what I will remember will be some moment with my girls, not signing the health care law or giving a speech at the U.N.

PG: I’ve probably watched too many YouTube videos of you lately, but as amazing as you’ve been in your pop culture moments — that tear for Aretha, singing “Let’s Stay Together” — I think you’re the first president in my life who is fully a man of his times. You’ve been the parents at Newtown, the boy who might have been Trayvon. You’ve been the Dreamers and their anxious parents. Has it been hard for you personally to represent such grief and hope?

BO: One thing you have to keep in mind is that I’m probably the most recorded, filmed and photographed person in history up to now. Because I’m the first president who came along in the digital age. Every leader is a funnel for the culture he lives in. And despite the exotic name and weird background, I grew up as an ordinary middle-class kid. The cultural touch points that shaped you are the same ones that shaped me. And the fact that that was true until I was 45 probably differentiates me from most presidents. For somebody like L.B.J., who fastened onto a political career early, it probably changed the way he experienced culture and presented himself. It never felt like a burden to me. What’s felt like a burden is seeing how politics has changed in ways that make it harder for Washington to work. There are a set of traditions, a constitutional design that allows someone like L.B.J. or F.D.R. to govern. And when those norms break down, the machinery grinds to a halt. That’s when you feel burdened. When you say, “Here’s what we need to do.” I’ve made my argument; the majority of the population agrees with me. Yet we’re confronted with endless filibusters and polarization that forbids us from getting stuff done.

PG: I don’t want to idealize the L.B.J. moment. There was a lot less equality for people of color and women. As a gay man, I don’t want to rocket back to 1964. But there was a common conversation on national issues back then. And it feels like we can’t have that anymore. We have Republican facts and Democratic facts, the relentless messaging of false facts. Any optimism here?

BC: I do. There’s no denying the polemic nature of politics has pushed everyone to the fringes. And the reaction to your administration has been an arms folded, “We’re not budging.” Instead of the horse-trading of L.B.J.’s time, giving this senator or that congressman what they needed to get where we need to go, we’ve turned to an athletic kind of partisanship. If you’re on the other side of the fence, I can’t support you even if you have a good idea. And the vitriol on the talking-head shows ——

PG: This doesn’t sound very optimistic.

BC: But it can be. Start right away. Do it with your friend. Disagree without being disagreeable. Don’t diminish him or her. Just work to find a common ground that we can build on.

BO: I just spoke to a group of young interns who rotate out every six months. They’re incredibly idealistic and motivated.

BC: And you crushed their spirit?

BO: I told them, if you had to choose a moment in human history to live — even if you didn’t know what gender or race, what nationality or sexual orientation you’d be — you’d choose now. There’s power in nostalgia, but the fact is the world is wealthier, healthier, better educated, less violent, more tolerant, more socially conscious and more attentive to the vulnerable than it has ever been. Now, there’s also enormous cruelty and tragedy and stupidity and pain. But we tend to forget what the world was like. I’m old enough to remember the ’70s, when we were still getting out of Vietnam, and we had lost tens of thousands of young soldiers. And when they came back home, they were completely abandoned. We left an entire swath of Southeast Asia in chaos. In Cambodia, two million people were slaughtered — about four times the number of people who have been killed in Syria during this conflict. But we don’t remember that.

BC: Were the kids surprised by your talk?

BO: I say this because I’m trying to inoculate them against cynicism, which is a powerful force in our culture. It’s what passes for wisdom, being ironic and cynical. Now, it’s true that the political landscape has changed in ways that are really unhealthy. But there are fewer lubricants to get things done. L.B.J. did great things, but he also relied on bagmen and giving them favors for which I would be in jail or impeached. People are surprised when I say that Congress is less corrupt now than it’s ever been.

But my optimism springs from the fact that ordinary people are less narrow-minded, more open to difference, more thoughtful than they were during L.B.J.’s time. The question for me is how do I grab hold of that goodness that’s out there and drag it into the political process? I think it requires some new institutional structure for more citizen participation than we’ve had in the past.

PG: Maybe tapping into the incredible power of pop culture?

BO: It’s a mixed bag. Michelle understood this earlier, because she had fewer resources. You have to leverage different platforms because a fireside chat just gets lost in the noise today. People aren’t part of one conversation; they’re part of a million.

PG: So, you go on Jimmy Kimmel?

BO: You’re drawing on where the culture is to get the message out. When I want to sign young people up for health care, I’ve got to do “Between Two Ferns,” which ended up being our biggest draw. Now, the flip side of this is the Trump phenomenon, where celebrity itself becomes a credential. If you are famous, then you have merit.

BC: And your opinion matters.

BO: I’m sure you’ve experienced this: The fact that you’ve now played a president almost qualifies you to be president.

BC: Wait a minute!

BO: It’s too late for this cycle.

BC: It could be a brokered convention. You never know.

PG: Last subject: Bryan’s movie made me rethink legacy. It’s not just the achievement; it’s the flavor of it, too. L.B.J.’s legacy is not just civil rights and Vietnam, but also his hunger to be loved and win. President Bush’s legacy is not only 9/11 and the Iraq War, but also his susceptibility to advisers. What’s the flavor of your legacy?

BO: Oh, it’s very hard for me to engage that.

BC: I can.

PG: You think it would be braggy?

BO: No, it’s that there’s me, and then there’s this character named “Barack Obama” who is slightly different on Fox News than he is on MSNBC. I wouldn’t vote for the Barack Obama on Fox News probably.

BC: He’s terrible.

BO: What a loser! No, it’s hard to see yourself in that way. The one area that I do feel confident about is the notion of an inclusive nation, that everybody is part of this story. That’s a running theme I’ve been faithful to throughout my presidency. I’ve given a lot of speeches. One of my favorites is one I gave in Selma, and there’s a riff when I talk about what America is. I’m talking about Jackie Robinson and a ranch hand, about an immigrant on the Lower East Side and a bunch of G.I.s landing on the shores of Normandy. I love it because it captures the essential miracle of this country: all these pieces from every corner of the globe. It works in fits and starts. It’s messy, and it’s ugly. There’s sadness and tragedy. Yet something distinctive and full of energy emerges from it. And it captures the imaginations of people all around the world.

PG: And that ties in with your work, Bryan.

BC: I don’t know about that.

PG: Of course it does. It’s the very inclusiveness that the president talked about, the range of humanity you show in your work.

BC: I’m just interested in telling good stories. And in essence, this is a good story. It’s why we talk about legacy. In sports, when someone retires, they don’t automatically elect them to the Hall of Fame. There’s a buffer period, a five-year period when everything has to settle down. After five years of being out of the limelight, do we still think of that person?

BO: Let me pick up on that. I was having a conversation with a couple of actors who were insisting that what they do is different from what I do. No doubt, it’s different. But never underrate the power of stories. Lyndon Johnson got the Civil Rights Act done because of the stories he told and the ones [Martin Luther] King told. When L.B.J. says, “We shall overcome” in the chamber of the House of Representatives, he is telling the nation who we are. Culture is vital in shaping our politics. Part of what I’ve always been interested in as president, and what I will continue to be interested in as an ex-president, is telling better stories about how we can work together.

BC: Well, I think your story is going to have a very happy ending.