Wyoming Republicans this week are considering a change to state election law that may make it harder for one of their own — Representative Liz Cheney — to win re-election next year.

The Wyoming Senate is set to hold a committee vote on Thursday on legislation that would require runoff contests after a primary election if no candidate wins a majority — a prospect that could doom Ms. Cheney by forcing her into a one-on-one contest with an opponent loyal to former President Donald J. Trump.

Ms. Cheney, who in January became the face of internal Republican opposition to Mr. Trump when she released a scathing statement announcing her vote to impeach him, has faced a significant backlash in her home state. Already, the Wyoming Republican Party has censured her, and there are multiple Republican candidates running against her, with Trump allies coming to the state to rally her opposition.

Donald Trump Jr., the former president’s eldest son, has since Monday posted two messages on Twitter in support of the legislation, saying lawmakers who oppose it are “turning their back on my father and the entire America First movement.” One of his tweets included contact information for state senators on the committee considering the proposal, which he claimed allies of Ms. Cheney were vying to thwart.

But in Wyoming, the situation is more complex. Republicans dominate politics there. Twenty-eight of the 30 state senators are Republicans, along with 51 of 60 state representatives. Mr. Trump won 70 percent of the state’s vote in November.

Republican contests often draw crowded fields — the state’s G.O.P. governor, Mark Gordon, won a six-way primary in 2018 with just 33 percent of the vote, then won more than two-thirds of the vote in the general election.

“We’re a major one-party state so whoever wins the primary is going to win the general,” Bo Biteman, a state senator who wrote the legislation, said in an interview on Tuesday. “This is just a different tactic to make more people happy with our primary system. It has nothing to do personally with Liz Cheney and the Trump supporters.”

Indeed, the proposal, which would move the state’s primary from August to May, with an August runoff in races where no candidate wins 50 percent, has support from some prominent Cheney supporters. State Senator Brian Boner, a co-author of the bill, backs the congresswoman. Matt Micheli, a former Wyoming Republican Party chairman, also favors both Ms. Cheney and the runoff proposal.

Wyoming Republicans said some state lawmakers opposed it because they preferred to campaign in the state’s warm summer months rather than in the spring, when the legislature is in session.

“I’ve seen no indication of Liz Cheney or any of her people in any way being involved in this legislation,” Mr. Micheli said. “As a conservative, this is something I’ve supported and thought would be a good idea for a long time.”

An aide to Ms. Cheney declined to comment. A spokesman for Mr. Gordon did not respond to requests for comment.

Mr. Biteman, who sought to overturn President Biden’s victory and said it was “best to keep my personal preferences to myself” about Ms. Cheney’s primary, said the Trump involvement in pressuring his colleagues to vote for the legislation has not been helpful.

“My poor colleagues on the committee, their phones were blowing up and they had thousands of emails,” he said. “One of the senators said to me in the hallway, ‘If I get one more call, I’m voting against the bill.’ I don’t know if that was a joke or not.”