WASHINGTON — House Speaker Kevin McCarthy is a man who stays in motion — enthusiastically greeting tourists at the Capitol, dashing overseas last week to the G7 summit of industrial world leaders, raising funds back home to elect fellow Republicans to the House majority.

But beneath the whirlwind of activity is a stubborn standstill, an imbalance of power between the far-right Republicans who hoisted McCarthy to the speaker’s role yet threaten his own ability to lead the House.

It’s a political standoff that will be tested anew as the House returns this week from a long summer recess and McCarthy faces a collision course of difficult challenges — seeking to avoid a government shutdown, support Ukraine in the war and launch an impeachment inquiry into President Joe Biden.

“They’ve got some really heavy lifting ahead,” said the No. 2 Republican in the Senate, John Thune, of South Dakota.

McCarthy, of California, is going to “have his hands full trying to figure out how to navigate and execute,” he said.

Congress has been here before, as has McCarthy in his nearly two decades in office, but the stakes are ever higher, with Republicans powered by an increasingly hard-right faction that is refusing to allow business as usual in Washington.

With former President Donald Trump’s backing, McCarthy’s right-flank pushed him into the speaker’s office at the start of the year only after he agreed to a long list of conservative demands — including the ability to call a quick vote to “vacate the chair” and remove him from office.

That threat of an abrupt ouster hovers over McCarthy’s every move, especially now.

To start, Congress faces a deadline to fund the government by the end of the month, or risk a potentially devastating federal shutdown. There’s just 11 working days for Congress to act once the House resumes Tuesday.

Facing a backlash from conservatives who want to slash government funding, McCarthy may be able to ease the way by turning to another hard-right priority, launching a Biden impeachment inquiry over the business dealings of the president’s son, Hunter Biden.

For McCarthy, running the two tracks — a government funding process alongside an impeachment drive — is an unusual and politically fraught undertaking.

But starting a formal impeachment inquiry into Biden could help to appease Republican allies of Trump, who has emerged as the GOP frontrunner to confront Biden in the 2024 election for the White House.

“He’s being squeezed,” Brad Woodhouse, a veteran Democratic operative, said of McCarthy. Woodhouse is now a senior adviser to the Congressional Integrity Project, which is preparing to criticize Republicans over the Biden impeachment.

The White House has said Biden is not involved in his son’s business dealings.

No Biden Wrongdoing Uncovered by GOP, So Far

But Trump’s allies among House Republicans are working furiously to unearth any links between Biden and his son’s business as they portray Hunter Biden as trading on the family name for financial enrichment and work to erode public support for the president ahead of the presidential election.

Republicans have not yet been able to produce evidence of wrongdoing by President Biden.

White House spokesman Ian Sams said, “Speaker McCarthy shouldn’t cave to the extreme, far-right members who are threatening to shut down the government unless they get a baseless, evidence-free impeachment of President Biden. The consequences for the American people are too serious.”

Meanwhile, what should have been a fairly prescribed process to fund the government after McCarthy and Biden negotiated a more than $1 trillion deal earlier this summer over the debt limit appears to be falling apart. Even a stopgap measure to simply keep government funding at existing levels for a few months while Congress tries to finish the spending bills is a nonstarter for McCarthy’s right flank.

Conservatives powered by the House Freedom Caucus are insisting federal spending is rolled back to 2022 levels and they want to add other priorities to the legislation.

If not, they say they will oppose a temporary measure, called a continuing resolution, or CR, to keep government running.

“We must rein in the reckless inflationary spending, and the out-of-control federal bureaucracy it funds,” the Freedom Caucus wrote in a statement at the end of August.

With command of dozens of votes, the hard right can deny McCarthy the support he needs to pass a Republican bill on its own. But relying on Democrats for votes would bring other problems for McCarthy if he is seen as disloyal to his ranks.

The conservatives want to beef up border security and address what Republicans deride as the “weaponization” of the Justice Department’s prosecutions, including of those charged in the Jan. 6, 2021 attack on the Capitol. They also want to end what they call the Pentagon’s “woke” policies as the Defense Department tries to provide diversity, equity and inclusion to service personnel.

Signaling the hard road ahead, Trump-ally Rep. Matt Gaetz, R-Fla., mockingly reposted one of McCarthy’s recent videos welcoming tourists at the Capitol.

“Kevin thinking this was the video we needed at this moment is depressingly revealing,” Gaetz said on social media.

“We need a SPEAKER not a GREETER.”

Congress also has a pending request from the White House to provide an additional $40 billion on three fronts — some $21 billion in military and humanitarian relief for Ukraine as it battles the Russian invasion; $12 billion to replenish federal disaster aids after floods, fires and other problems, including to curb the flow of deadly fentanyl at the southern U.S. border with Mexico.

McCarthy has vowed there won’t be any “blank check” for Ukraine as he works to appease skeptical Republicans who want to end U.S. involvement in overseas affairs, particularly involving Russia.

While the shutdown is the more pressing problem for McCarthy, the Biden impeachment inquiry is his bigger political gamble.

McCarthy has signaled an impeachment inquiry is coming. But there is “no date circled on the calendar,” said a person familiar with his thinking and granted anonymity to discuss it.

Not all House Republicans are eager for impeachment proceedings. “We can waste our time on issues that are not important, or we can focus on issues that are,” Rep. Ken Buck, R-Colo., said Sunday on MSNBC’s “Inside with Jen Psaki.”

Trump faces his own more serious charges of wrongdoing, including the federal indictments over his efforts to overturn the 2020 election he lost to Biden and his refusal to return classified documents stored at his Mar-a-Lago estate. He has been indicted four times this year.

Watching from the Senate, which has been working to pass all 12 of the regular bills needed to fund government operations through committees ahead of floor votes starting next week, Republicans hope cooler heads in the House will prevail on all fronts.

Several Republicans have made no secret of their disinterest in impeachment proceedings against Biden.

And GOP Sen. Lisa Murkowski said those who don’t think a federal shutdown of government operations is a big deal ought to visit her state of Alaska and see “real life.”

During a previous government shutdown, Murkowski said crab fisherman couldn’t get out in the water because federal permits could not be issued.

“You know, we’ve got a lot of things going on here in the Congress right now,” she said. “So the House is going to have to sort through their priorities and hopefully, they’re going to be priorities that are in the best interests of the operations of good governance.”