In Washington, Republicans are particularly concerned about a handful of extreme-right House members who could run for Senate in swing states, potentially tarnishing the party in some of the most politically important areas of the country. Mr. McConnell’s political lieutenants envision a large-scale campaign to block such candidates from winning primaries in crucial states.

But Mr. Trump’s political cohort appears no less determined, and his allies in the states have been laying the groundwork to take on Republican officials who voted to impeach Mr. Trump — or who merely acknowledged the plain reality that Joseph R. Biden Jr. had won the presidential race.

Republicans on both sides of the conflict are acknowledging openly that they are headed for a showdown.

“Hell yes we are,” said Representative Adam Kinzinger of Illinois, one of the 10 House Republicans who voted to impeach Mr. Trump…

“In 2022, we’ll be faced with the Trump pitchfork crowd, and there will need to be an effort to beat them back,” Mr. Reed said. “Hopefully they’ll create multicandidate races where their influence will be diluted.”