As Taylor Swift’s N.F.L. adventure began in earnest at a Kansas City Chiefs game against the Chicago Bears on Sept. 24, the reaction of the Fox broadcast crew — and much of the N.F.L. world in general — was summed up by Erin Andrews, a veteran sideline reporter.

“We all need to calm down,” Ms. Andrews said, shortly after Travis Kelce scored a second-half touchdown.

Ms. Andrews was making a nod to one of Ms. Swift’s songs, but she was also acknowledging how star-struck she and her colleagues were to have the world’s biggest pop star at Arrowhead Stadium to see her new love interest, Mr. Kelce, play for the Chiefs. Greg Olsen, the lead analyst on the broadcast, went as far as bragging that Ms. Swift had once liked one of his tweets.

While Ms. Swift’s presence dramatically expanded the audience for Chiefs games — Nielsen Media Research estimated an additional two million women watched Kansas City’s game on Oct. 1 — some backlash was inevitable. Ms. Swift joked about “pissing off a few dads, Brads and Chads” in her Time Person of the Year profile, but she had run out of one-liners (and facial expressions) by the time the comedian Jo Koy, in a disastrous hosting gig at the Golden Globes, said: “The big difference between the Golden Globes and the N.F.L.? At the Golden Globes, we have fewer camera shots of Taylor Swift.”