House Republicans are barreling ahead this week with their plan to oust Representative Liz Cheney of Wyoming, their No. 3, from her leadership post, the latest sign of the immense sway former President Donald J. Trump continues to hold over the party.

Representative Kevin McCarthy, the minority leader, on Sunday officially endorsed Representative Elise Stefanik of New York to replace Ms. Cheney, the Republican conference chairwoman. Ms. Stefanik has revived Mr. Trump’s false claims about the 2020 election, while Ms. Cheney has drawn fire from Mr. Trump and others in the party for repudiating those lies. The vote is expected on Wednesday.

“Yes, I do,” Mr. McCarthy told the Fox News host Maria Bartiromo when she asked whether he supported Ms. Stefanik’s bid.

“We need to be united, and that starts with leadership,” Mr. McCarthy said. “That’s why we will have a vote.”

The choice to stick with Ms. Cheney or remove her is widely seen as an indicator of the path the party will take in the post-Trump era. Will it return to the conservative tradition represented by Ms. Cheney, the daughter of a Republican vice president? Or will it continue marching in lock step with Mr. Trump — who remains popular with the Republican base even though the party lost the House, the Senate and the White House during his tenure — no matter how outlandish his claims?

Critics of Ms. Cheney insist that the vote is also about a lack of message discipline as the party heads into the 2022 midterm elections. While many Republicans quietly agree that President Biden was legitimately elected and that Mr. Trump bore some blame for the Jan. 6 attack on the Capitol, they say they would rather focus on countering Mr. Biden’s agenda instead of purging their party of lies and extremism.

For days, Mr. McCarthy has been working behind the scenes on behalf of Ms. Stefanik, who has a less conservative voting record than Ms. Cheney but has increasingly aligned herself with Mr. Trump. Mr. Trump and Representative Steve Scalise of Louisiana, the No. 2 House Republican, have also endorsed her.

Representative Jim Banks of Indiana, the chairman of the conservative Republican Study Committee, who has sponsored legislation with Ms. Cheney opposing troop reductions in Afghanistan, made the case against her on “Fox News Sunday.”

“Right now, it’s clear that she doesn’t represent the views of the majority of our conference,” he told the show’s host, Chris Wallace.

Some House Republicans tried to oust Ms. Cheney from her leadership post in February after she voted to impeach Mr. Trump for his role in inciting the attack on the Capitol. Ms. Cheney easily turned back that challenge — winning a 145-to-61 caucus vote — after Mr. McCarthy delivered an impassioned speech in her defense.

But now it is other Republicans who are rallying to her side.

Senator Bill Cassidy of Louisiana, who also voted to convict Mr. Trump in his second impeachment trial, argued that the party needed to adopt a bigger-tent philosophy in which both supporters and critics of Mr. Trump were welcome.

“You look at polls, there’s a whole group of folks that agree with Liz Cheney, and so for us to win in 2022 and 2024, we need everybody,” Mr. Cassidy said Sunday on NBC’s “Meet the Press.”

Representative Adam Kinzinger, Republican of Illinois, pointed out that Mr. McCarthy had said Mr. Trump bore responsibility for the Capitol riot — only to later insist that others stop talking about it.

“For me, I’m a conservative,” he said during an interview on CBS’s “Face the Nation.” “I’m going to fight for the soul of this party. But every member, not just leadership, every congressman, every state representative, every member of the party that pulls a ballot in the primary has to decide, are we going to exist on lies or exist on the truth?”