Like an exhausted marathon runner, Kevin McCarthy had just about staggered across the finish line. But even at 2.11am, with tempers frayed and eyes bleary, the newly elected speaker of the US House of Representatives wanted to single out one person for praise.

“I do want to especially thank President Trump,” McCarthy told reporters after prevailing in the longest election for speaker since before the civil war. “I don’t think anyone should doubt his influence. He was with me from the beginning.”

The gushing tribute obscured the complexity of Donald Trump’s intervention in the election for speaker – and what sway he might hold over the narrow Republican majority in the new Congress.

The week that followed brought a series of extremist actions and appointments that appear designed to resonate with his rightwing base. But whether House Republicans’ agenda will ultimately complement or conflict with Trump’s 2024 presidential election campaign remains uncertain.

McCarthy’s election as speaker took four gruelling days, 15 roll call votes and concessions that he might come to regret. Trump’s endorsement appeared impotent for much of that time, even among some of the former president’s champions in Congress. As he made calls in the dying hours of Friday night, a memorable photo showed Congresswoman Marjorie Taylor Greene attempting to give her phone, with “DT” on the line, to colleague Matt Rosendale, only for him to wave it away.

But in the end, Trump’s man won – a sign that he remains important if not decisive. McCarthy duly felt obliged to heap praise on the kingmaker. He also made a somewhat optimistic claim: “This is the great part: because it took this long, now we learned how to govern.”

That was immediately put to the test. On Monday evening, Republicans passed legislation to cut funding that was intended to bolster the Internal Revenue Service on a party-line vote. The speaker proclaimed: “Promises made. Promises kept.” Democrats called it a deficit-raising windfall for wealthy tax cheats at the expense of the majority that has no chance of passing in a Senate they still control.

On Tuesday, Republicans formed a panel to tackle what they perceive as rampant abuse of power in the federal government, not least by law enforcement agencies investigating Trump’s attempts to overturn the 2020 election results and handling and storing of presidential records at his Mar-a-Lago residence in Florida.

The subcommittee focusing on “the weaponization of the federal government” falls under the judiciary committee, headed by Congressman Jim Jordan of Ohio, who has repeatedly said Trump should become president again. It will have access to classified information, a privilege usually reserved for the intelligence committees in the House and Senate.

Its “investigate the investigators” mandate was doubtless music to the ears of Trump, who has spent years airing grievances at rallies about a “deep state” conspiracy that led to the Russia investigation and two impeachments. Democrat Jamie Raskin, a prominent member of the now dissolved January 6 committee, called the new panel an “insurrection protection team”.

On Wednesday, Republicans targeted abortion. Their majority passed a resolution to condemn attacks on anti-abortion facilities, including crisis pregnancy centers, and a separate bill that would impose new penalties if a doctor refused to care for an infant born alive after an abortion attempt. Neither is expected pass the Democratic-led Senate.

The moves were condemned by liberals but did not go as far as some conservatives would have liked – a tacit acknowledgment that abortion has become politically awkward for Republicans since last year’s supreme court decision that overturned Roe v Wade after half a century. Trump has blamed anti-abortion hardliners for Republicans’ disappointing midterm elections results.

Larry Sabato, director of the Center for Politics at the University of Virginia, said: “Would you start with that, if you were in their position, having just lost a midterm election effectively because of the abortion issue? What was that doing there in the first place? Forty-eight hours of the actual Congress and this unorganized? Just amazing. There must be a stupidity chemical in the Washington water system.”

McCarthy also spent the week fending off questions over calls for fabulist New York congressman George Santos to resign and the deal he struck with the House Freedom Caucus during his epic election battle. Like the Tea Party before it, the House Freedom Caucus is fixated on small government and less spending. Media reports suggest that it intends to seek cuts to entitlement programs such as social security and Medicare as well as to defense and law enforcement.

It is all part of an “extreme Maga Republican agenda”, according to Democrats.

Chuck Schumer, the Senate majority leader, said in a statement: “In the last week Republicans have given a free pass to wealthy tax cheats, empaneled a committee to undermine and threaten law enforcement, undercut women’s healthcare, and put forward a draconian budget plan that will lead to cuts to Medicare and social security and defunding the police.”

There was a further statement of intent in House committees. Despite claiming to have embraced diversity and inclusion, Republicans named fewer women as committee chairs than men named Mike. The new chairs also have records that suggest they are ready to push Trump’s “Make America great again” agenda.

Jordan, leading the judiciary panel, has amplified Trump’s “big lie” that the 2020 election was stolen and refused to comply with a subpoena issued by the January 6 committee over his communications with the former president.

The new chair of the oversight committee, James Comer, has co-sponsored a national abortion ban that could have imprisoned doctors, amplified false claims of voter fraud in the 2020 election and called attempts to investigate the January 6 insurrection a “political stunt”, “a big show” and “illegitimate”.

Jason Smith, chair of the ways and means committee, has supported cutting social security and Medicare, voted to overturn the 2020 election and described the January 6 committee as a “sham” that was “designed to attack President Trump”. Jodey Arrington, chair of the budget committee, has adopted similar positions.

Mark Green, chair of the homeland security committee, has introduced legislation to build a border wall and called for the homeland security secretary, Alejandro Mayorkas, to resign. He has also asserted that being “transgender is a disease” and said America must “take a stand on the indoctrination of Islam in our public schools”. Green identifies as a creationist and has argued against the theory of evolution.

At first glance, it has the makings of a Trump caucus ready to do its master’s bidding and aid his run for the White House. Joe Walsh, a former Republican congressman, said: “Most of what they’re going to focus on is a bunch of revenge stuff for Trump, for how they believe Trump was treated, and a lot of this culture war bullshit.

“I’m convinced that a big part of what all these investigations involve is a lot of these guys believe the 2020 election was stolen from Trump: the FBI did it, the justice department did it. Trump and the Republicans declared war on the FBI some years ago so they’re going to go after them.”

That McCarthy credited Trump with helping him secure the gavel “tells you exactly still where Trump stands in the party”, Walsh added. “McCarthy said that publicly, which is why Trump is still the king of the GOP hill unless something happens.”

It was McCarthy who initially condemned Trump over the January 6 assault on democracy only to then make a pilgrimage to Mar-a-Lago a few weeks later and signal that all was forgiven. Now that Trump has backed McCarthy for speaker, despite significant opposition from his own base, he might expect the California Republican to repay the favour in 2024.

But Henry Olsen, a senior fellow at the Ethics and Public Policy Center in Washington, has doubts. “McCarthy is going to go where the winds blow,” he said. “To begin with, as a speaker he has to recognise where everyone in his conference is so he could very easily tell Trump at least during the early part of 2023, ‘Look, I’ve got a five-vote majority. I’ve got people who love you, I’ve got people who hate you, you know I love you but I’ve got to keep this group together.’

“He may not like that but, if McCarthy did anything other than that in the initial jousting phases of the primary, McCarthy would be a poor political strategist. And McCarthy may lack certain attributes necessary to be a speaker but reading the room is not something he lacks.”

There are other icebergs on the horizon. Congress faces an agenda of must-pass bills to fund the government, resupply a military depleted by decades of war and support for Ukraine, authorise farming programmes and raise the nation’s borrowing limit to avert a disastrous federal default. In this context, an obsessive Republican pursuit of dead-on-arrival bills and Biden investigations could backfire on Trump.

Elaine Kamarck, a senior fellow at the Brookings Institution thinktank in Washington, said: “Between opposition within their party, between the Senate and the presidency, they’re not going to win anything. What it’s going to do is be a constant reminder to people of the extremes of the far right and Trump is so firmly associated with them. Substantively they’re alike but stylistically they’re alike as well. It’s bad for him. It paints him into a real corner.”

Kamarck, who served in Bill Clinton’s White House, added: “The thing that was amazing about his presidency was that, unlike any other president before him, he did not ever seek to expand his base. He was purely and simply happy with his factional base. The demographics of his factional base are that they’re old so every year that he relies on that base gets more and more problematic.

“He’s simply weak. And he’s going to have challengers for the 2024 Republican nomination which will make him look weaker.”