After having kept Liz Cheney in leadership, Republicans are faced with questions about Marjorie Taylor Greene’s future in the caucus.

WASHINGTON — Riven by infighting over the future of their congressional leadership and their rank and file, Republicans are torn over how aggressively to confront the rise of far-right extremism and the influence of former President Donald Trump in their ranks.

A pair of colliding controversies is pushing Republicans into separate camps and forcing their leaders to pick sides, with high stakes for the party’s future.

“This isn’t about one member. It’s about what we stand for and whether we want to be a serious party going forward,” said Republican consultant Brendan Buck, a former aide to the party’s last two House speakers.

One controversy centers on first-term Rep. Marjorie Taylor Greene of Georgia, who faces rising criticism for having elevated calls for violence against Democrats on social media and for espousing grotesque theories that the terrorist attacks of Sept. 11, 2001, and the mass shooting at a high school in Florida in 2018 were staged.

The other centers on Liz Cheney of Wyoming, the third-ranking House Republican, who castigated Trump and voted to impeach him last month.

On parallel tracks, calls for Greene’s expulsion and Cheney’s ouster from leadership intensified in recent days and came to a head during a House Republican Conference meeting Wednesday evening.

House Minority Leader Kevin McCarthy, R-Calif., told members that he didn’t plan to remove Greene from her committees. Then the caucus voted 145-61 by secret ballot to keep Cheney in leadership, a lopsided vote that suggests some private disenchantment with Trump in the caucus.

The clash over Greene, who has been raising money over the controversy and has refused to apologize publicly, has put McCarthy in a predicament. And it is unlikely to go away, as the Democratic-led House plans to vote Thursday on a resolution to remove Greene from the Education and Labor Committee and the Budget Committee.

It’s not just Democrats who say Greene is a problem.

Senate Minority Leader Mitch McConnell, R-Ky., issued an unusual statement Monday condemning Greene for espousing “loony lies and conspiracy theories” that he said were a “cancer for the Republican Party and our country.” At the same time, McConnell praised Cheney, a daughter of former Vice President Dick Cheney, as a strong leader in the party.

A former Republican leadership aide said McConnell’s commentary is “instructive for McCarthy” in terms of taking clear stands.

“Instead, [McCarthy is] letting the House Republicans bleed out right now every day that this continues,” the former leadership aide said on condition of anonymity to avoid angering McCarthy.

McCarthy’s handling of the issue is being closely watched in all corners of the party, and it will set a precedent for radical figures who may be eying running for office — and weigh on voters who are torn about whether to support Republican candidates again.

“The House GOP seems only intent on what’s good for winning a primary, and McConnell is trying to win back a majority,” Buck said. “We cannot win back college-educated suburban voters without making clear this is not a party of conspiracy theorists and nuts.”

Greene claims to have the support of Trump. She has become the face of the so-called QAnon faction of the party, which includes a group of his supporters who promote online conspiracy theories that Trump has been facing down a cabal of Democrats and celebrities who engaged in child sex trafficking.

She claimed Wednesday that she is being victimized because of her identity as white, Christian and conservative, among other things.

Dan Eberhart, a major Republican donor, said: “Republican leaders follow their voters, not the other way around, and the base isn’t there yet on tossing Trump overboard. The Republican Party is no longer run by the elites in Washington. It’s run by the grassroots activists at the state level, and they aren’t listening to Washington. They are listening to people like Representative Greene.”

McConnell told reporters Tuesday that he wants to create distance between Greene and the rest of the party.

“I did, yesterday, express myself on that particular new member of the House. And I think I adequately spoke out about how I feel about any effort to define the Republican Party in such a way,” he said. “I think that pretty well covers my view on that.”

McConnell associates say he saw fringe figures (like Christine O’Donnell and Todd Akin) win Republican Senate primaries in 2010 and 2012 and then cost the party winnable seats when they lost in their general elections. He doesn’t want to allow that again.

In recent years, McConnell has also raised alarms about the party’s weakness in the suburbs, and the associates say he views it as detrimental if the party is seen as connected to QAnon.

A Morning Consult/Politico poll released Wednesday found that Greene is becoming a household name, with 46 percent of registered voters saying they have views about her — a rise of 21 points since August. And Democrats are increasingly working to paint the entire Republican Party with her brand of radicalism.

“Republicans have a choice: Are they going to stand with QAnon and a member in their midst who has advocated for violence and extremism, or are they going to embrace truth, honesty, integrity and accountability?” Rep. Debbie Wasserman Schultz, D-Fla., said Wednesday on MSNBC. “The ball is in their court. And unfortunately, the House will have to act if they don’t.”

Sen. Mitt Romney, R-Utah, the party’s 2012 presidential nominee, said the GOP “isn’t big enough to have both conservatives and kooks.” He said the party “should have nothing to do with Marjorie Taylor Greene” and that it “should repudiate the things she said and move away from her.”

But others who have courted voters on the hard right are treading more cautiously, including Sen. Lindsey Graham, R-S.C., who said he wants her to explain herself.

“Are these postings accurate? I want to hear from her. Before I want to judge what to do about her, I want to know what the facts are. If these are not accurate postings, they’ve been manipulated, I’d like to know that,” Graham told reporters Tuesday.

When told that she is on video making some of the claims, Graham said: “She’ll have to tell me: Is it accurate? I don’t know. I haven’t seen the video, what’s accurate, what’s not.”