Mr. Norton said he believed Mr. Meijer made a mistake in blaming Mr. Trump for inciting the riot.
“We have a lot of people with a lot of passion and we can’t control everybody,” he said, before going on to exaggerate the pockets of unrest that took place alongside last year’s largely peaceful protests for racial justice. “Blaming President Trump is the same thing as blaming Kamala Harris and Joe Biden for all the riots that antifa did last summer.”
Representative John Katko of Central New York, who was the first G.O.P. lawmaker to back impeachment, is one of the few remaining Republicans who represents a Democratic-leaning district. Some Republicans in his district were outraged by his vote.
“‘Not very happy’ would be the politest way to say it,” said Fred Beardsley, the chairman of the Oswego County Republican Committee. “We’re very upset. I’m tremendously upset.”
“I think Mr. Katko crossed a line,” he continued. “He double-crossed us.”
For Mr. Katko and Representatives Adam Kinzinger of Illinois, Anthony Gonzalez of Ohio, David Valadao of California, and Fred Upton and Mr. Meijer of Michigan, all Republicans who voted for impeachment and hail from states likely to lose seats in this year’s redistricting process, the shapes of the districts they may seek to represent in 2022 have yet to be determined.
Democratic state legislators in New York and Illinois could draw Mr. Katko and Mr. Kinzinger into districts represented by fellow incumbent Republicans, potentially cutting off a path for a Trumpian insurgent, while commissions will determine district lines in California, Michigan and Ohio.
Gene Koprowski, a conservative filmmaker who filed to run against Mr. Kinzinger, said he did so to start raising money but he is waiting for the Illinois legislature to redraw its congressional district maps before formally beginning a campaign.
Challengers to Ms. Cheney, who represents the single at-large Wyoming district, don’t face the same calculation. Anthony Bouchard, a state senator, announced his campaign on Wednesday as President Biden was being inaugurated. By Thursday night, he was a guest on Newsmax TV and Laura Ingraham’s program on Fox News.