Ms. Cheney, a longtime Republican, said that the G.O.P. “has rejected the Constitution in the name of supporting Trump” and that Mike Johnson should not be speaker.

Former Rep. Liz Cheney (R-Wyo.) indicated in an interview at The Capital Times Idea Fest in Madison, Wisc., that conservatives could end up forming a new kind of conservative party, arguing that “far too much has happened that’s too damaging” in the Republican Party.