As the House of Representatives prepares to return from its six-week vacation, Speaker McCarthy’s job looks more imperiled than at any time since he won the gavel in January. Competing demands from House conservatives and Republican senators — coupled with a Democrat in the White House — will make it nearly impossible for the speaker to satisfy all sides while dodging a vote of no confidence. 

On Tuesday, the House will be in session for the first time since July 27, when the Republican leadership failed to advance any of Congress’s key funding measures. Now, with just weeks to go before a possible government shutdown, Mr. McCarthy’s burden hinges on whether he can keep his more conservative members in line. 

Two key House caucuses — the Freedom Caucus and the Republican Study Committee, which together boast more than 200 of the House’s 222 GOP members — have already said they will not pass a short-term funding bill, known as a continuing resolution, unless aggressive cuts are made to food stamps and Ukraine aid, and unless discretionary spending limits are capped. 

In order to win the speakership earlier this year, Mr. McCarthy had to acquiesce to a number of conservative demands, including the stipulation that the House pass all 12 appropriations bills individually rather than rushing through a budget negotiated behind closed doors with hours to go before the deadline, as has been typical in the past. Only one of the 12 bills has been passed by the House so far. 

When Mr. McCarthy and President Biden reached a debt ceiling deal earlier this year, they agreed that if all 12 bills were not signed by December 31, then there would be an automatic cut in spending of 1 percent across the entire federal government. 

The spending limits Mr. McCarthy agreed to with the president, though, have now left House conservatives dissatisfied. As part of the debt limit deal, the two men stipulated that all non-defense discretionary spending would be cut for 2024 and 2025 and then be limited to 1 percent growth until 2029. According to the Congressional Budget Office, the deal would cut $64 billion from discretionary spending in 2024 and $107 billion in 2025. 

The Democratic Senate, though, is already charting its own path, with Republicans and Democrats working together to boost aid for Ukraine and ignore most of the House GOP’s spending caps — something that would be a nonstarter for conservatives in the lower chamber.

One influential congressman, French Hill, said he and his colleagues need to advance more “conservative” spending bills than the Senate so that they have some “negotiating clout” before a government shutdown. 

“We don’t control the Senate, we don’t control the White House, but what we do control is our own appropriations process,” Mr. Hill said in an interview with CBS. The House Appropriations Committee “has written more conservative bills and more conservative funding levels than the Senate,” he added, urging that the remaining bills be passed quickly. “But to have that negotiating clout, we need to get all those bills passed across the House floor.” 

He says that gives the Senate “a distinct advantage over the House in the negotiation for 2024 spending details. And if we want to merit that, and have the right kind of negotiation that House conservatives want, then we need to come together and pass those 11 bills as soon as possible.” 

The shape of the final legislation, written after the House and Senate complete the process of reconciling the appropriations bills, cannot be known without the House setting its own limits. Whatever comes out of the conference process, though, is unlikely to satisfy any of the House conservatives who have demanded ending aid to Ukraine as a prerequisite for supporting Mr. McCarthy’s legislation and him as speaker. 

As part of his deal to have conservatives end their blockade of his candidacy for speaker in January, Mr. McCarthy also agreed to lower the threshold for the “motion to vacate,” or a vote of no confidence, to just one member — meaning that any member of Congress can go to the House floor and force Mr. McCarthy to win back his position. 

The other problem for Mr. McCarthy is that he must satisfy conservative demands for an impeachment inquiry into Mr. Biden, something he has suggested is likely but still remains widely unpopular according to polls, and could be a difficult lift for the 18 Republican representatives who currently serve districts that the president won in 2020. 

Some moderate members of the GOP conference — and even one leading conservative — have said they are unlikely to support an impeachment of Mr. Biden. One Biden-district Republican, Congressman Mike Lawler, said “we’re not there yet” when asked about impeachment. Another representative from a district won by Mr. Biden, Congressman Don Bacon, said he has yet to see evidence of high crimes and misdemeanors.

“I think before we move on to [an] impeachment inquiry, we should … there should be a direct link to the president in some evidence,” Mr. Bacon told The Hill. “We should have some clear evidence of a high crime or misdemeanor, not just assuming there may be one. I think we need to have more concrete evidence to go down that path.”

Even a member of the Freedom Caucus, Congressman Ken Buck, has said an impeachment inquiry is unnecessary because multiple House committees are already investigating the president and his family. “This is impeachment theater,” Mr. Buck told the Hill. “I don’t think it’s responsible for us to talk about impeachment. When you start raising the ‘I-word,’ it starts sending a message to the public, and it sets expectations.”