But Mr. Brady — perhaps at the suggestion of his wife, Gisele Bündchen, who said she and her husband did not vote for Mr. Trump in 2016 — later kept his distance. When the Patriots won the Super Bowl in 2017, Mr. Brady did not attend the subsequent reception at the White House.
Mr. Brady and Ms. Bündchen have in recent weeks reportedly hired divorce lawyers.
Then there’s the idea that Mr. DeSantis, a Harvard- and Yale-educated former college athlete who has privately teased a 2024 presidential run, needed help spelling the name of the most storied stadium in the National Football League — and a hallowed place for many voters in a critical presidential battleground state. At least Mr. DeSantis didn’t need help pronouncing Lambeau, a name that has tripped up past presidential aspirants.
For Mr. Michels, whose campaign also did not respond to inquiries about his remarks, it is good but perhaps risky politics to seek a friendship with Mr. Rodgers, himself a Super Bowl-winning quarterback (albeit only once, to the consternation of much of Wisconsin) who is unquestionably the most popular figure in the state.
Mr. Rodgers, like Mr. Brady, has dabbled in politics with some complications. In 2011, he supported unionized public school teachers in their fight with Gov. Scott Walker. Later, he said the quarterback Colin Kaepernick belonged in the N.F.L. after Mr. Trump called for his banishment for kneeling during the pregame playing of the national anthem to protest police violence against Black people.
But last year, Mr. Rodgers, who refused to be vaccinated against Covid, became a source of misinformation about the vaccines. That made him a hero to Wisconsin’s fellow vaccine skeptics, in particular Senator Johnson, who thanked him “for his courage in defending personal freedom and health autonomy.”
This month, Mr. Johnson campaigned with Packers fans while wearing Mr. Rodgers’s jersey.
Mr. Michels, who is locked in a tight battle with Gov. Tony Evers, a Democrat, was with Mr. Johnson outside Lambeau Field, though he was conspicuous in his lack of Packers gear. A local Democrat pointed out that Mr. Michels, a Wisconsin native who spent more than a decade living in Connecticut and Manhattan before moving back home to run for governor, was wearing a green vest that was the shade worn by the visiting Jets, not the hometown Packers.