Speaker Kevin McCarthy returns to Washington this week confronting a twin set of challenges: avoiding a costly government shutdown and addressing growing calls on the right to impeach President Joe Biden, despite resistance from the party's moderates.

Congress is already facing a chaotic work period, with a looming deadline at the end of the month to fund the government, reauthorize the Federal Aviation Administration, and deal with the White House's request for disaster relief and aid for Ukraine. But further complicating matters in the House is a demand from hardliners to hit the gas on impeachment, as well as looming threats to McCarthy's speakership if he breaks his promises to members of his right flank.

And those storms are set to collide, with House members such as Rep. Marjorie Taylor Greene making her support for government funding contingent upon the House GOP launching an impeachment inquiry into Biden, among other things.

"I personally would like to see the inquiry happen (this) week," the Georgia Republican told CNN. "Our conference needs to stop capitulating to the left, more members that are in blue districts. That's not what the donors are donating money for. And we need to stop allowing Biden-district Republicans to hold up our agenda."

Adding to McCarthy's headaches: an increasingly agitated Donald Trump is set to forcefully weigh in on those topics this week as part of an expected media blitz, according to multiple GOP sources familiar with his plans. The former president is likely to ramp up his calls to impeach Biden and come out strongly against Ukraine aid, further ratcheting up pressure on McCarthy as he plots his strategy for the treacherous month ahead.

All of this is expected to be discussed in a closed-door party meeting Wednesday, the first time House Republicans will huddle in person since before the six-week August recess. How McCarthy and his leadership team handles this critical month of governing will have major implications for both the country and his speakership.

"Once again, it's going to be another major leadership challenge to be able to kind of thread the needle on some very important issues that are up against the clock," veteran GOP Rep. Steve Womack of Arkansas told CNN. "And I worry that the country is going to suffer as a result of our inability to, you know, get our act together and define consensus among ourselves. ... It's a mess right now."

Some members -- particularly those who serve on spending panels -- are openly expressing frustration that leadership hasn't sorted out these issues in a more timely manner, putting them up against the clock.

"We have done our job," GOP Rep. Tony Gonzales of Texas, who like Womack serves on the House Appropriations Committee, told CNN. "And it's time for House leadership to do its job and get these bills passed."

But allies note McCarthy has successfully navigated tricky political headwinds before, from his weeklong battle to clinch the speaker's gavel to negotiating a bipartisan deal to raise the debt ceiling, which enraged House conservatives. And they're confident he can emerge unscathed once again.

"McCarthy is good at this," GOP Rep. Dusty Johnson of South Dakota told CNN. "He's been dealt an incredibly difficult hand. But he, I think, for the last nine months has played that hand as well as any human being in the House can. I continue to have a high level of confidence in his leadership, and most everyone I've talked to feels the same way."

'We're on different planets'

McCarthy's spending strategy has started to come into focus. Sources say he is considering moving a short-term funding bill with disaster aid while leaving the Ukraine money for a separate fight, in which he is hoping to extract key wins on border security that members of his right flank have been pushing for. On a recent conference call, sources say McCarthy floated the idea of a one-month patch -- a continuing resolution, or "CR" -- to keep the government funded at current levels until November.

But even that plan is riddled with potential hurdles. The White House and Senate leaders from both parties are insisting Ukraine aid be attached to the short-term funding bill, putting the two chambers on a potential collision course. The Senate could add the Ukraine money to the temporary funding patch and send it back to the lower chamber, but that could risk a shutdown if House Republicans dig in.

It's also unclear if leaving out Ukraine aid from the temporary funding patch will be enough to appease conservatives in the House, who are making a host of demands in the funding fight, from tightening border security to defunding parts of the Department of Justice.

McCarthy has tried to implore members to save those battles for later in the year, but not everyone is buying the argument.

"Leadership has made it clear that they would prefer a clean CR to continue the negotiations and feel like policy riders should be part of the conversation about funding bills, not CRs," GOP Rep. Ben Cline of Virginia, a member of the far-right House Freedom Caucus, told CNN. "But for us in the Freedom Caucus, we don't see reasons why we shouldn't talk about policies being added to a CR conversation."

And there could be even bigger problems down the road, when the House and Senate try to find consensus on long-term funding bills. The two chambers are hundreds of billions dollars apart and divided over controversial social issues that House Republicans have tacked on to their spending bills.

"We may be in the same galaxy, but we're on different planets," said Womack. "There's a danger in moving in a direction that is far different than the Senate. And that is you got to be able to deliver on your own, and we haven't demonstrated the capacity to put 218 votes on the board."

Johnson emphasized that compromise from both House Republicans and Senate Democrats will be necessary, telling CNN, "You can't fund the government with a Senate work product or a House work product. You need a joint work product."

For some, though, even talk about a short-term funding bill is a nonstarter, making the threat of a government shutdown more of a reality.

"I am against a continuing resolution in any form or fashion," Gonzales told CNN. "If it's for a day, if it's for a month, if it's for a year, if whatever trinkets get thrown in there. I'm completely against a continuing resolution because we've talked about this forever. We have to get back to regular order."

When asked if he felt Congress was careening toward a government shutdown, Gonzales said, "It certainly feels that way."

"The writing has been on the wall for weeks now where the game has essentially been whose fault it is, not who's going to solve it. It's this hot potato."

Some hardliners are threatening to tank a procedural vote for a short-term spending bill, which would prevent it from coming to the House floor. And there has been renewed talk of forcing a vote to remove McCarthy as speaker if he is seen as violating his spending promises or giving too much to Democrats, as CNN previously reported, though hardliners have previously backed off such threats.

Asked whether it was a tool he was willing to use, GOP Rep. Bob Good of Virginia told Fox Business: "Everything is on the table to hold the speaker accountable, to do what he committed to do back in January."

Impeachment calls grow louder

Hanging over it all is the question of whether and when House Republicans will move forward with a Biden impeachment -- which Democrats have insisted is nothing more than a political ploy, given the House GOP has yet to prove allegations that Biden directly profited off his son's foreign business deals.

Over the August recess, the impeachment drumbeat inside the Republican conference has only grown louder, with even reliable McCarthy allies like Greene insisting on holding a vote to authorize an inquiry when lawmakers return to Washington.

"Put the vote to the floor, even if it fails. I guarantee you, if you put it back, it'll pass because every single Republican that votes no to it will get destroyed by their districts," Greene told CNN.

While McCarthy has called an impeachment inquiry a "natural next step" in Republicans' investigations into Biden and his son, the speaker doesn't have the votes to proceed. A number of moderates and even GOP Rep. Ken Buck of Colorado, a member of the House Judiciary Committee -- where impeachment articles originate -- are openly opposed to such a move. One moderate GOP lawmaker said they believe there are as many as 30 Republicans who don't believe there's enough evidence yet for impeachment, based on informal conversations with colleagues.

Johnson, who chairs the centrist-leaning Main Street Caucus, is one of them.

"There is a constitutional and legal test that you have to meet with evidence," Johnson told CNN. "I have not seen that evidence, but I guess I'm not suggesting it doesn't exist. I do think the fact that the committees continue to ask for additional documents suggests that they don't think their evidentiary record is complete yet."

Some GOP senators have warned House Republicans about the dangers of pursuing impeachment.

Sen. Marco Rubio, a conservative Florida Republican, said that while an impeachment inquiry can be useful to get information that the Biden administration has refused to turn over, he added: "I still think it's a dangerous."

Rubio told CNN: "They're an extraordinary measure, they should not be routine."

West Virginia Republican Sen. Shelley Moore Capito was even more direct.

"We got so many things we need to be focusing on," Capito said when asked about impeaching Biden. "I don't see the glaring evidence that says we need to move forward. I didn't see it in the Trump case and voted against it. I don't see it in this case."

McCarthy has vowed to hold a floor vote to formally authorize an inquiry if Republicans go that route, meaning 218 votes will be necessary to begin the process. But leadership has not yet formally whipped on the issue, though there have been informal temperature checks. The hope from supporters of an impeachment effort is that launching an inquiry would help get skeptics on board with impeachment articles.

"That's my thinking," said Cline, who supports moving forward with an impeachment inquiry. "An inquiry would clarify the facts and what has happened and what evidence is still remaining that needs to be obtained by the committees."

But GOP Rep. Matt Gaetz of Florida, long a thorn in the side of leadership, is done waiting around. He signaled he wants to force a floor vote on impeachment as soon as Congress returns this week, and made a not-so-veiled threat to McCarthy's speakership over a number of grievances, including on the issue of spending.

While any single member can force a floor vote to oust McCarthy, thanks to a deal he made to become speaker, it would still require a majority of the House to actually remove him.

"We've got to seize the initiative. That means forcing votes on impeachment. And if Speaker McCarthy stands in our way, he might not have the job long," Gaetz wrote on social media last week.

Johnson warned that any effort to remove McCarthy as speaker would be "dangerous for our country."

"We need a unified Republican team piling up conservative wins," Johnson said. "And, you know, spending weeks engaged in a leadership battle would put everything else on the backburner."

House Republican leadership was able to stave off a snap impeachment vote earlier this summer when GOP Rep. Lauren Boebert of Colorado attempted a similar move, but the stakes are higher now for McCarthy. Gaetz's warning, considered an empty threat by McCarthy allies at this point, could become more real as the situation plays out and demands are not met.

If McCarthy again defers an impeachment vote, it could enrage the right. But if he allows it to proceed, it would likely fail -- and put all his members on the record over the issue.

"I would say that any reputable governing majority is not going to put something on the floor if they don't have the votes. That would just be kind of stupid in my opinion," Womack said. "So I don't think anything's gonna happen until you have some kind of a reliable whip (count)."