After a bruising fight over the House speakership, newly empowered Republicans officially set to work this week on what they say is a mandate to hold Joe Biden and his administration to account.

Several of the president’s chief antagonists took control of powerful committees, eager to use their subpoena power to frustrate and undermine the president, his administration and his family.

Republicans approved the formation of a subcommittee on the “weaponization of the federal government”, to serve as a main vehicle for scrutinizing the administration. They launched an investigation of the Afghanistan withdrawal and commissioned a panel to look into the government’s response to the coronavirus pandemic. At least one Republican filed articles of impeachment against Biden’s secretary of homeland security, Alejandro Mayorkas, over his handling of migration at the southern border.

On Friday, ​the House judiciary committee​, led by Jim Jordan of Ohio, a fierce ally of Donald Trump, ​​opened an investigation of Biden’s handling of classified documents​,​ vowing an aggressive inquiry into a matter Republicans hope will damage the president as he prepares ​​a likely re-election bid.

​After a chaotic start marked by infighting and discord, Republicans appeared to have unified around a common target: Biden.

In his first remarks as speaker, Kevin McCarthy said Republicans would “be a check and provide some balance on Biden’s policies”, using the “power of the purse” and the “power of the subpoena”.

Yet even as ​Biden’s political foes threaten to ensnare him in a web of politically charged investigations and high-stakes legislative brinkmanship, the president himself has embraced a less confrontational approach, focused on promoting his achievements and touting bipartisanship.

“Now the House has elected a new speaker,” Biden said, “and I called and congratulated him and I’m ready to work with him or any Republican in Congress to make progress for the American people.”

​On Friday, the White House said Biden accepted McCarthy’s “kind invitation” ​to deliver a State of the Union address​ on 7​ February.

Whether such shows of comity lead to bipartisan cooperation, political conflict or both will prove a critical test for Biden in a divided government over the next two years.

Far-right Republicans who won concessions from McCarthy in exchange for their support for speaker have raised the specter of government shutdowns or even a debt-default as a means of forcing spending cuts, and vowed to examine the business dealings of the president’s son, Hunter Biden. Some have called for the president to be impeached.

Americans should brace for a “period of ugly conflict” in Washington that echoes early clashes between Bill Clinton and the Republican speaker Newt Gingrich, whose party stormed to victory in the 1994 midterms, said Russell Riley, a presidential historian at the University of Virginia’s Miller Center.

Gingrich’s conservative majority ushered in an era of political gridlock that culminated in a 21-day shutdown. But, Riley said, Clinton presented himself as the “voice of reason”, demonstrating a willingness to compromise but not capitulate. He easily won re-election in 1996.

Barack Obama also played on themes of Republican intransigence to win re-election in 2012, after Democrats lost the House in 2010.

Riley, who has examined how presidents navigate divided government, said a hostile Republican House could prove an effective foil for Biden should he seek a second term.

“This will be a burden to Biden in the short-run – he’s yoked by the constitution to a dysfunctional governing partner – but it will benefit him in 2024,” he said. “Most of the country will not rally to the incendiaries.”

Biden sought to offer a contrast last week, visiting a dilapidated bridge in Kentucky to tout a $1.2tn infrastructure bill signed into law with Republican support, even as McCarthy suffered rounds of humiliating defeats in his quest to be speaker. Biden was joined by the Senate minority leader, Mitch McConnell, and other Republicans.

The president then traveled to the US-Mexico border, as Republicans blame his immigration policies for the record number of migrants crossing into the country. This week, Biden wrote a Wall Street Journal op-ed that urged Congress to work together to hold big tech accountable.

“There will be many policy issues we disagree on in the new Congress,” he wrote, “but bipartisan proposals to protect our privacy and our children; to prevent discrimination, sexual exploitation, and cyberstalking; and to tackle anticompetitive conduct shouldn’t separate us.”

Biden has emphasized his willingness to work with the Republican House but he has also drawn red lines. A slate of tax-related proposals, he said, would make inflation worse.

“I’m ready to work with Republicans but not on this kind of stuff,” Biden said on Thursday, promising a veto.

The White House also shot down any suggestion it would circumvent Congress to avoid a debt-default.

“Attempts to exploit the debt ceiling as leverage will not work,” the press secretary, Karine Jean-Pierre, told reporters. “There will be no hostage-taking.”

‘Always a double standard’

The discovery of classified documents at Biden’s home in Delaware and an office in Washington has already pushed his relationship with hostile House Republicans into further jeopardy. On Thursday, the attorney general, Merrick Garland, appointed a special counsel to investigate the matter. Biden said he was “cooperating fully and completely”.

Republicans seized on the revelations, accusing Biden of hypocrisy for his criticism of Trump after FBI agents retrieved classified materials from the former president’s Mar-a-Lago estate in Florida.

“There’s always a double standard,” tweeted Steve Scalise, the House majority leader, asking: “Where’s the raid of Biden’s garage?”

Though such attacks ignore the significant legal differences between the two cases, they have nevertheless energized Republicans determined to puncture Biden’s stretch of good fortune after a historically strong midterm performance by Democrats.

In November, Democrats expanded their Senate majority and blunted losses in the House, despite Biden’s low approval ratings and widespread economic angst. Emboldened by the elections, Biden said he saw no reason to change his approach.

He has argued that support for his agenda, including a hard-won health and climate law passed despite unified Republican opposition, would only grow as the policies take effect over the next two years.

“We’ve made some real progress,” Biden said before a cabinet meeting last week. “But now we need to focus on implementing the big laws we actually passed so that the American people can feel the benefits of what we’ve done.”

Still, a divided Congress leaves little opportunity for progress on campaign promises Democrats were not able to enact when they controlled both chambers. Progressives are calling on Biden to use executive actions to prove his commitment to issues he ran on in 2020 and to make the case for 2024.

Progressive lawmakers have called on the president to take action on issues including climate, abortion, workers’ rights and marijuana reform.

“In the last Congress there were definitely moments when President Biden was holding back on executive action to leave lots of room and space for Congress to act,” said Mary Small, national advocacy director of Indivisible, a progressive grassroots organization.

“None of that should be happening now.”