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(CNN) -- House Democrats have begun internal debates about how to deal with the prospect of a chaotic situation: the possibility that House Speaker Kevin McCarthy will lose his seat in an unprecedented vote on the floor.

Although no decision has been made, some of the party's moderates are privately signaling that they would be willing to strike a deal to help McCarthy avoid a right-wing revolt, as long as the president meets his own demands.

Publicly, Democratic leader Hakeem Jeffries has not commented on how he would like his peers to handle a challenge to McCarthy's presidency, saying it is hypothetical at this point. But privately, Jeffries has advised his members to keep the powder dry, according to multiple sources, an acknowledgment that it is best for Democrats to keep their options open while a fight over government funding takes place.

"If Democrats are somehow asked to help, it won't have to be just out of the goodness of our hearts," Democratic Rep. Dan Kildee of Michigan told CNN. "If Kevin can't govern with his side alone — which he clearly can't — and he wants to have a conversation with us about how to do that, we're going to have a conversation about policy."

Asked by CNN recently if he would need the help of Democrats to save him, McCarthy declined to comment.

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"I'm not worried," he said.

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Private discussions have gathered steam in recent days, as a handful of GOP hardliners entrench themselves against a series of spending bills — an effort that could catapult the government into a shutdown — and when any action the president takes to advance a short-term spending bill with Democrats could trigger the end of his presidency.

If McCarthy's job were threatened by an impeachment motion, and there were five Republicans backing it, Democrats would have a major role in deciding McCarthy's fate.

But congressmen who spoke to CNN made clear that any Democratic aid would come at a cost. According to Democrats, the price they are asking for saving his office is a bipartisan agreement to avoid a government shutdown, a path McCarthy is not yet willing to take, as Republicans are still trying to reach consensus on a GOP plan to fund the government.

"I think it's fair to say that Democrats have a responsibility to prepare for the possibility that there is some kind of disruption," one Democratic member told CNN.

One of the strategies Democrats are considering is to vote "present" or vote in favor if a motion to impeach McCarthy is presented. Voting "present" would change the threshold and make it harder for McCarthy's critics to remove him, which would require a majority of voters to succeed.

It's a tricky dance for Democrats, who don't want to be seen as saving McCarthy — especially after he just launched an impeachment inquiry against President Joe Biden — and one that could expose them to reaction from the left. But some Democrats also fear the possible alternative: a government shutdown and the possibility that an even more right-wing lawmaker could ascend to the presidency if McCarthy is impeached, or that the House would be paralyzed without any candidate being able to get 218 votes to be elected president.

"If he just bogs us down with something horrible, and they're still trying to impeach him, and that's going to be his focus for working with the Freedom Caucus, there's less incentive (to help him)," one Democrat said. "Still, even then, you're going to have a lot of people say, 'Well, I think what's behind door No. 3 could be a lot worse.'"

"I think if he's willing to collaborate on things," the congressman said, adding, "We'll be enough to protect him."

It's not yet clear when or if McCarthy's detractors will try to push the issue. Republican Rep. Matt Gaetz of Florida, one of McCarthy's staunchest critics, declined to specify Wednesday when he would try to force a vote to remove McCarthy as House speaker. But he warned McCarthy against working with Democrats, saying House Republicans working with Democrats to prevent a shutdown would be signing their own "political death warrant."

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"If Chairman McCarthy trusts the Democrats to pass a continuing resolution, he would call the moving truck from the Capitol to his office very soon because my expectation would be that he would be out of the president's office fairly promptly," said Gaetz, who privately told colleagues Wednesday that there are seven Republicans who would vote against any disruption measures. enough to end it if all Democrats oppose a conservative plan.

With less than two weeks before a government shutdown, Democrats are watching the president's actions on spending carefully and considering whether McCarthy is willing to cut off his losing flank in the pursuit of a bipartisan agreement on spending — short-term on Capitol Hill as a continuing resolution or a CR — in consideration of how they would act on the floor if a motion to dislodge.

"If we were really part of the deal, as part of a commonsense agreement on the CR and the budget, I think there would be a significant group of people willing to vote for it," one Democrat said.

House Minority Leader Hakeem Jeffries, left, and House Speaker Kevin McCarthy, a California Republican, right. (Credit: Getty Images)

In search of a bipartisan agreement

Meanwhile, frustration in the Republican Party has reached its peak, private conversations between moderate Democrats and Republicans about a bipartisan funding deal have become more serious: The bipartisan Problem Solvers Caucus has developed a framework for a plan, and Jeffries stopped by its meeting on Wednesday.

Leaving the meeting, Jeffries called for a bipartisan agreement along the lines of what was already negotiated in the debt ceiling package, an agreement cut by McCarthy but later abandoned under pressure from his right flank to seek deeper cuts.

"We have to find a bipartisan agreement consistent with what was previously reached," he said.

But the mechanism for introducing such a bill is complicated. One possible option is for Republican members of the group to sign the so-called discharge petition, a complicated and lengthy procedural mechanism. If five Republicans did so, it would trigger a process that could force a vote on the bill without McCarthy having to. But that process would likely take too long at this point to avoid a shutdown.

Members are also discussing other procedural options with the House parliamentarian, lawmakers told CNN.

"Failure is not an option. We're going to do everything we can to avoid a shutdown," said Republican Rep. Don Bacon, who represents a decisive district in Nebraska.

Bacon warned he would strike a deal with Democrats if they reach an impasse with hardline conservatives.

"Well, in the end, if not, we will have to work through the corridor and get it. I think people have gotten that message," he said.

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But the growing consensus is that, with time running out, the most viable path to avoid a government shutdown is for the president of Congress to shed his right flank and strike a deal with the center, and then Democrats could rescue McCarthy from the inevitable impeachment vote that would be triggered in that scenario.

Democrats considering rescuing McCarthy say they wouldn't necessarily stop there.

"We're having pretty broad conversations about how to use imagination to reframe this place that's not working," the member said. "I don't think it's something as transactional as 'okay, I vote on my bill and that's it,' because you can't trust it. I think then it becomes everything from what committee presentation is to how bills get to the floor and how those decisions are made."

However, an opportunity to extract concessions from McCarthy would probably never be enough for some Democrats. For Democrats, extending a lifeline to McCarthy could mean facing a challenge in their party's primaries, not to mention the fact that any goodwill McCarthy may have still had with some Democrats evaporated with his announcement that he was launching an impeachment inquiry.

"There is not a single chance that I will vote for the president. I have hardly any words. What reasonable thing has he done? What demonstrable approach has he made to try to bring the House together, to work together in a deliberative and cooperative way?" said Democratic Rep. Debbie Wasserman Schultz of Florida. "The real answer is that right now I don't see a scenario where he would deserve my support, but I wouldn't say never."

Democratic Rep. Dean Phillips of Minnesota recently said "right now, no," that neither he nor other Democrats would come to McCarthy's rescue if he faced an impeachment motion from his own party.

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"If you had asked me two months ago, I would have said absolutely. But I think unfortunately their behavior is unprincipled and not helpful to the country," he said.

He continued: "I understand the position you are in, but these are times when people have to choose. Do you please a few or do you take care of the majority?"

Several Democrats argued that previous Republican leaders in the House — such as Paul Ryan or John Boehner — might have deserved to be saved. But McCarthy, they argue, is different.

If McCarthy were impeached, it would only take a handful of Democrats to save him. In addition to voting "present," they could also vote in favor of introducing the resolution, a procedural solution that would essentially kill the initiative. However, letting Democrats vote alone could be politically dangerous for moderates. Voting in unison with Democrats could protect members of the base.

"I think we have to have a party position on this. I don't think it's been resolved yet. It's still evolving," Democratic Rep. Richard Neal of Massachusetts told CNN.

Many Democrats are still weighing their options.

"There are so many variables right now that I don't really have an answer," Rep. Mary Gay Scanlon of Pennsylvania told CNN.

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