House Speaker Kevin McCarthy is seen in Statuary Hall in the US Capitol building in Washington, DC, on March 10.
CNN  — 

Rep. Marjorie Taylor Greene has a blunt message for House GOP moderates: Impeach President Joe Biden or face a fierce backlash from voters next year.

“What’s going to hurt them is not supporting articles of impeachment,” Greene, the Georgia firebrand, told CNN.

On the other side: Republicans in swing districts wary of the tactics embraced by Greene and others on the far right as they push their conference in a sharply conservative direction and away from the bread-and-butter issues they sold to voters.

“I’m frustrated because I want to focus on the things that I was sent here to do,” said GOP Rep. Anthony D’Esposito, a freshman from a New York district that Biden carried by 15 points.

And caught in the middle: House Speaker Kevin McCarthy who owes his narrow majority to the 18 Republicans who won in those districts Biden carried – but has increasingly been forced to cater to the evolving demands of the right wing of his conference, putting swing-district Republicans in a jam.

Matt Gaetz, the Florida conservative, is not too concerned.

“It’s actually going to be a new doctrine for us,” Gaetz said of the use of so-called “privileged” resolutions to force floor votes on thorny issues like impeachment and censuring House members, which two hard-right congresswomen pursued in the last week and put some Republicans in a difficult spot.

McCarthy on Thursday told CNN that such moves “probably won’t go anywhere” if members go rogue and don’t brief other House Republicans.

“Because I think we work as a team, not individuals,” he said.

Balancing the competing and often conflicting demands of his conference has been a familiar script for McCarthy since winning the speakership on the 15th ballot in January. And for the first five months of the year, he managed to limit dissension as they pushed through messaging bills on parental rights, border security and energy policy. Republicans close to the speaker say his goal is to keep open a line of communication with members, something his leadership team is weighing as they look to brief their conference after the July Fourth recess on the spate of investigations into Biden.

But after McCarthy was forced to cut a deal with Biden to raise the nation’s borrowing limit, he has faced growing angst from members on his far right who were unhappy with the deal, with the fiercely conservative lawmakers pushing for deeper spending cuts, faster-paced investigations and a snap impeachment of Biden.

Adding to the challenges: Rivalries between conservative members eager to outmaneuver one another, underscored by Greene calling Republican Rep. Lauren Boebert of Colorado “a little bitch” on the House floor for moving unilaterally to circumvent the leadership and force a vote to impeach Biden. Greene now is drafting up five impeachment resolutions on Biden and other officials, such as Attorney General Merrick Garland and FBI Director Chris Wray, and plans to force a House vote on them as well.

Greene told CNN that the tension with Boebert has “been building for quite some time,” contending that she tried to team up with her colleague on an impeachment resolution but was ignored — only to see Boebert blindside her colleagues and try to force a vote on her own plan this week.

“I’ve donated to her. I’ve supported her. I’ve defended her when she’s been attacked. It’s never been reciprocated, even though it should have been,” Greene said. “So she copied my impeachment articles and probably did it, it seems to me, because there’s a fundraising deadline coming up at the end of the month.”

As hard-right members are prepared to use every tactic they can to get their way, many in the GOP conference are perplexed.

“If all you provide is messaging bills, and all you do is stop rules votes from going through and things like that, we will not succeed in two years,” said Rep. Don Bacon, whose Nebraska district Biden won by six points. “But I believe we will succeed because the majority of us do know that we have to govern, and governing means that you have to work with Democrats.”

Some of the more moderate members want McCarthy to take a firmer line with lawmakers in the House Freedom Caucus, arguing that giving in to their demands only gives them incentive to continue to try to drive the conference further to the right and undercut their efforts to show unity. But as a result of a deal he cut to win the speakership, any one member can call for a vote seeking his ouster, something some on the far right have floated.

One GOP member, granted the condition of anonymity to speak freely, argued that the recent strategies used by the right flank are more about raising campaign cash and making splashy headlines than about pursuing a serious agenda, or going through the regular order process they fought for in the speaker’s race.

“All of a sudden they throw a temper tantrum and don’t care if it goes through the regular order process they fought for,” the member told CNN. “It’s becoming quite clear the hypocrisy.”

GOP battles grow after debt ceiling deal

The internal battles have only intensified since the debt limit law was enacted.

Just this month, the House was paralyzed for an entire week by a handful of conservative rebels who voted against a procedural rule to consider legislation, a tactic rarely employed by the majority party.

“What floor activity?” GOP Rep. Ken Buck of Colorado quipped about the lack of legislative action recently, making the broader point that most bills passed in a Republican controlled House are dead on arrival in the Senate anyway.

The hardliners ultimately relented after McCarthy accepted deeper domestic spending cuts than outlined in the bipartisan debt limit deal he cut with the White House, setting up a major government funding clash later this year.

Then, as his conference had hoped to focus its message on issues such as battling Biden’s student loan forgiveness program and combating illegal immigration, the focus instead shifted to Rep. Adam Schiff after a conservative freshman, Anna Paulina Luna, forced a vote to censure the California Democrat over his handling of the Trump-Russia probe, a rare reprimand by the House typically reserved for the most severe of offenses.

Not to be outdone, Boebert drafted a privileged resolution to impeach Biden over his handling of the situation at the border – a vote that could have made Republicans appear to be shielding the president if they opposed the dramatic step of accusing the president of high crimes and misdemeanors.

“I am concerned,” said Rep. Tony Gonzales, a Texas Republican, when asked about being forced to take a vote on impeaching Biden. “One witch hunt for another witch hunt makes this place all about witch hunts. Meanwhile, the American public are focused on putting food on the table, keeping their kids safe in schools, keeping inflation down. Real issues.”

Greene claimed that members have to take the matter of impeachment into their own hands and bypass the committee process because she was told last week by House Judiciary Chairman Jim Jordan, whose panel would oversee any impeachment effort, that he does not have the votes among House Republicans on his panel to advance impeachment proceedings.

Jordan told CNN of the tactic to force the Biden impeachment vote, “I think there’s a better way to do it,” while still vowing to support it.

But while many members argue that voting to impeach Biden before conducting an investigation undercuts the effort, Gaetz argued that the procedural tool Boebert used this week to try to force an impeachment vote is well within the House rules. And he’s done waiting for others, even leadership, to get on board.

“I sort of have had enough struggle sessions,” he said. “I’m ready for action, action, action.”

To avoid a messy floor fight, McCarthy and his aides had to resort to negotiating on the House floor Wednesday night with Boebert and other members who supported her effort to force an impeachment vote on Biden, where a deal was ultimately struck to refer Boebert’s resolution to the House Homeland Security and Judiciary committees, something Boebert promised to take credit for, according to a source familiar with their conversation.

That allowed Republicans to show some unity on the divisive matter – at least for now.

“I am a sophomore congresswoman, and I have learned very early that nothing happens in this town without force,” Boebert said Thursday. “I called up my privileged resolution and forced people to make tough decisions.”

And she warned: “If I don’t see accountability taking place with Joe Biden in a timely manner – and no, I don’t have a date, deadline – but if I see that this has been slow rolled and nothing is moving on it, then there’s always the option to bring up another privileged resolution and call to impeach Joe Biden.”

Not everyone is on board – at least not yet.

“We were elected on issues related to the economy, border security and public safety – but also accountability,” said Rep. Nick LaLota, the New York Republican who won a district Biden narrowly carried. “Whenever we come up with these issues, it goes through the committee, it’s well-vetted, the facts are understood and the public is part of the process.”

CNN’s Morgan Rimmer contributed to this report.