Their fund-raising dwarfed by their Democratic rivals, Republican nominees including Blake Masters and Mehmet Oz have been in Washington gathering cash from lobbyists.
Ms. Hageman’s victory in Wyoming means Ms. Cheney will soon lose her perch in Congress, where she has been fighting a figure she believes poses a grave threat to American democracy.
Interviews at polling places in Wyoming’s bluest county, Teton, where Ms. Cheney lives, turned up a stream of voters re-registering as Republicans.
If Representative Liz Cheney loses her primary on Tuesday, as is widely expected, the Cowboy State’s conservative tilt will take on a harder edge.
The Republican says her crusade to stop Donald J. Trump will continue — even if she loses her primary next week. Restoring a “very sick” G.O.P. will take years, she says, “if it can be healed.”
For Republicans, anemic fund-raising, missteps by Donald J. Trump and weak candidates could stand in the way of bigger statehouse gains in November.
The former vice president is part of a group of Republicans who have visited early nominating states as they weigh a challenge to their party’s most dominant force.
House Democrats have been pressing the president to come up with a bumper-sticker-worthy slogan. The White House says it’s sharpening its message.
Senator Mitch McConnell had been trying to recruit Gov. Doug Ducey of Arizona to run, but former President Donald J. Trump had warned him against it.
The 87-year-old Republican has told people that he will step down at the end of the year, four years before his term is up. His seat is likely to stay in G.O.P. hands.