Those races, in Alaska, Georgia, North Carolina, Wyoming and elsewhere, promise to amplify calls for election audits, claims of fraud and a recasting of events surrounding the Jan. 6 riot at the Capitol. That debate will test the extent to which embracing Mr. Trump’s falsehoods about the 2020 election — and attempts to downplay the violence that followed — has become a new litmus test for Republican voters.

“It still is a burning ember of passion for the base,” said Matt Batzel, the national executive director of American Majority, an organization that trains conservative grass-roots activists. “If those in Washington try to move on, there is going to be even a greater disconnect and greater frustration with their leadership, resulting in more tension and arguments within the party.”

That prospect is alarming for some Republicans who worry about the long-term consequences of embedding Mr. Trump’s false claims into the foundation of the party. Far more Republicans, however, expressed concern this week about the near-term consequences: With President Biden’s approval ratings falling well below half of voters, many Republicans fear that debate will be a distraction ahead of a 2022 midterm election in which they are otherwise well positioned to take back power.