Just minutes after Speaker Mike Johnson breathed a sigh of relief after quashing a short-lived conservative revolt and winning re-election to his office on Friday, far-right lawmakers sent him a letter.

It wasn’t a congratulation.

They only voted for him, they wrote, “because of our unwavering support of President Trump and to ensure the timely certification of his electors.”

“We did so despite our serious reservations about the speaker’s track record over the last 15 months,” lawmakers from the ultra-conservative House Freedom Caucus continued, attaching a list of three key complaints against Mr. Johnson and seven policy imperatives they believe demanded of him.

Welcome to the 119th Congress.

“I just expect intramural wrestling matches to be somewhat of the norm,” said Rep. Mark Amodei, Republican of Nevada, as he left the House after Mr. Johnson’s surprise election as speaker.

Since ascending to the top job in the House of Representatives after many of those same conservatives ousted his predecessor, Mr. Johnson has had one of the most difficult jobs in Washington. Now, with Republicans in full control of government and President-elect Donald J. Trump’s vast domestic agenda at stake, he faces his toughest test yet.

Mr. Johnson will be responsible for pushing through Mr. Trump’s economic plans, including one or more major bills that lawmakers say will simultaneously raise the country’s borrowing limit, extend the tax cuts signed by Mr. Trump in 2017 and cut federal spending. and implemented a sweeping crackdown on immigration.

At the same time, he will have to deal with a capricious president who has already shown a penchant for stalling congressional negotiations at the eleventh hour and introducing new demands. And he will do so while trying to lock down an unruly group of lawmakers who, despite their reverence for Mr. Trump, have already shown a willingness to defy him on key votes and who care little about the political consequences of an upset within the USA party.

Within weeks, Mr Johnson’s majority will shrink even further. He loses two reliable Republican votes, Reps. Elise Stefanik of New York and Michael Waltz of Florida, who are leaving the House to work in the Trump administration, meaning he can only afford a single exit with tight vote counts.

There are also huge expectations about what Mr. Trump can achieve with a Republican trifecta.

“I never said the other things we were going to do were going to be easy; They will actually be very tough,” said Republican Rep. Carlos Gimenez of Florida. “But we have to do it for the American people. The American people expect us to accomplish something, and I think that will be the driving force. Every now and then we have to take a hard vote.”

Mr. Johnson’s allies like to say never bet against him, a refrain they repeated after the speaker, a Republican from Louisiana, was re-elected on Friday after a single, albeit tortured, ballot.

But it was clear that the fight in the House over Mr. Johnson’s ascension to speaker was just the opening salvo in a fight brewing over the tax, budget and immigration bills that Republicans wanted to pass.

Among the key demands issued by the Freedom Caucus in the House of Representatives on Friday was that the bill “not increase the federal debt” – a move that Mr. Trump has urged House Republicans to approve – “before real spending cuts are agreed upon and be implemented”.

They also complained that Mr Johnson had failed to promise to ensure that “any reconciliation package reduces spending and the deficit in real terms in the light of the dynamic assessment of tax and spending policy in the light of recent growth trends”.

Such demands will almost certainly spark a bitter dispute among House Republicans over how to structure Mr. Trump’s supposedly landmark legislation. It is estimated that just extending the tax cuts that Trump signed in 2017 will cost about $4 trillion. Offsetting those cuts — as well as any immigration measures that Republicans are also clamoring to enact — would result in deep spending cuts that could draw a lot of interest from more moderate Republicans who are sure to have their say.

Some mainstream conservatives, who just won tough reelection battles in swing districts and preserved the Republican majority in the House, have already vented their frustration with their hardline colleagues.

“It angers the 95 percent of us that 5 percent would do this to Mike Johnson — and the entire conference; Who are you?” said Representative Don Bacon of Nebraska. “We are the 95 percent, and these people act like they’re some upper house or something from the conference. And we don’t like that.”

“We’ve had enough of these guys,” he added. “Most of us don’t want to work with them, we don’t want to work on their legislation because it’s all about them.”

That may be fine with them, but it will only make Mr. Johnson’s job of cobbling together a Republican majority on Mr. Trump’s priorities even more difficult.

Rep. Ralph Norman of South Carolina, one of two Republicans who initially opposed Mr. Johnson for speaker of the House on Friday only to then change his vote, told reporters that his message on the tax and budget bill was – that this was possible and would ultimately not cost the taxpayer any money.

“I think Mike Johnson now knows that won’t be the case,” Norman said, adding that he respected how the speaker handled his concerns.

“He said, ‘Look, if I don’t show up like I say I will and push forward with the things you’re saying, you’re going to screw me over,'” Mr. Norman continued. “He said, ‘I never thought I’d get this job anyway.'”

Karoun Demirjian And Maya C. Miller contributed to reporting.