WASHINGTON >> Hours after winning control of the House, Republicans began laying out plans Thursday for investigations of President Joe Biden, his administration and his family, and were met with promises of a multimillion-dollar counteroffensive from a network of groups allied with Democrats.

On Capitol Hill, the incoming Republican chair of the House Oversight Committee, Rep. James Comer of Kentucky, said the panel would focus on trying to link Biden to the business dealings of his son, Hunter Biden, continuing an effort begun in 2018 that never established the elder Biden’s complicity in any wrongdoing but led to former President Donald Trump’s first impeachment.

Comer told reporters his aim was “to show you this is an investigation of Joe Biden,” and not just his son.

The Hunter Biden investigation is only one element of a broader planned effort by House Republicans to use their new oversight powers to examine a wide range of Biden administration figures and policies.

The White House, which is building its own defense team, has quietly signaled support for some of the efforts by nonprofit groups with ties to some of the biggest donors in Democratic politics, according to people familiar with the groups.

The efforts appear intended to take pressure off the administration by pushing back in a more adversarial manner than Biden’s team on sensitive subjects, including the U.S. withdrawal from Afghanistan, the administration’s COVID response and — perhaps most notably — the foreign business dealings of Hunter Biden.

“The White House cannot be the sole nucleus for publicly responding to the onslaught of congressional investigations,” reads a memo from a nonprofit group called Facts First USA that has been circulating among major Democratic donors, members of Congress and others.

It details a $5 million-a-year “SWAT team to counter Republican congressional investigations,” including on issues that “may be too personal or delicate for the White House to be responding or to even be seen as directing a response” — an apparent reference to Hunter Biden.

David Brock, the Democratic activist behind Facts First, said his group “intends to work with the White House where appropriate but will make our own judgments.”

Another group, the Congressional Integrity Project, announced Wednesday that it intended to launch a multimillion-dollar “war room” to undermine investigations from the House. People involved in that initiative, which was first reported by Politico, have previously worked with Brock’s team and have close connections to the White House and the Democratic Party.

The political arm of the Center for American Progress, the influential progressive think tank, is planning to cast the Republican investigations as “politically motivated revenge politics,” according to its CEO, Patrick Gaspard, who served as White House political director under President Barack Obama.

The rush by some of the left’s leading figures to organize swift responses to potential investigations highlights an old Washington dynamic: When there is divided government, lawmaking tends to grind to a halt and Congress is dominated by oversight fights.

That is likely to be particularly true when Republicans take control of the House of Representatives next year with a majority that is slimmer than the party had hoped. In such an environment, it can be easier to win support for oversight investigations, which require less consensus than major legislative initiatives.

Republicans appear to be divided on just how far to push things. Kevin McCarthy, the Republican nominee to be speaker of the House, has downplayed an impeachment of Biden, even as some on the far right in his party have called for such an effort as payback for the two impeachments by Democrats of Trump.

But Republican leadership has not ruled out impeaching Cabinet members, including Department of Homeland Security Secretary Alejandro Mayorkas and Attorney General Merrick Garland, who have both recently fortified their staffs to deal with the challenge.

Moreover, McCarthy, Comer and Rep. Jim Jordan, the incoming chair of the House judiciary committee, have made it clear they intend to aggressively pursue investigations into Hunter Biden, the crisis at the border and the Justice Department, which Jordan accused of operating as a political arm of the White House.

Jordan said the focus of his committee would be “the political nature of the Justice Department and the linkage now to what was happening with the Hunter Biden story.”

Jordan declined to say if he had evidence that Garland, or any other officials at Justice Department headquarters, had sought to influence federal prosecutors in Delaware investigating Hunter Biden. Comer, for his part, conceded that his effort to raise awareness of the issue faced public skepticism, although he blamed Democrats for devaluing the committee’s work.

“I realize that congressional oversight doesn’t have a lot of credibility,” he said.

Biden’s allies hope to stoke that distrust further, deploying the financial muscle of new outside groups like Facts First, funded by “dark money” from donors whose identities can be kept secret. The law enforcement inquiries into two figures who loom largest in the oversight investigations — Hunter Biden, who is under investigation for tax-related violations and other issues, and Trump — add another layer of intensity to the fight.

Trump declared his candidacy for the 2024 presidential election Tuesday, even as he faces investigations related to his handling of classified materials, his efforts to overturn the results of the 2020 election and his business.

While some in the party blame him for disappointing results in this month’s midterm elections, his allies in Congress have indicated that they intend to use the oversight investigations to damage the president and avenge Trump.

House Republicans have been working closely for months with outside groups affiliated with Trump and funded by anonymous cash to plan for the oversight.

The White House declined to comment.

But it has been compiling research on Republican arguments and the members of Congress making them, including trawling deeply conservative corners of the internet to build out a rapid-response database, according to a person familiar with the effort.

The White House also added lawyers and communications staff members, while working with outside lawyers to prepare for an anticipated barrage of subpoenas, as well as possible efforts to impeach Joe Biden. An administration official said that additional personnel would be added to handle the inquiries in the White House and the agencies under Republican scrutiny, including the departments of Defense, Education, Health and Human Services, Homeland Security and State.

“Republicans are going to launch baseless broadsides against the White House,” Eric Schultz, who handled the Obama administration’s response to congressional oversight investigations, said in an interview. “They already have been. Holding them accountable for their own word as a measure of their credibility, that’s entirely fair game.”

Hunter Biden will be assisted in the congressional investigations by Joshua A. Levy, who previously represented the opposition research firm Fusion GPS when it became the target of Republican congressional investigations.

Levy declined to comment.

Kevin Morris, a Hollywood lawyer who has been helping Hunter Biden with financial and legal support, offered to collaborate with the Facts First effort during a meeting in September in Los Angeles with Brock, according to people familiar with the meeting.

Morris has assembled a team of lawyers, computer forensic experts and public relations professionals, according to a person familiar with Morris’ plans. They have discussed plans to go on offense against allies of Trump who targeted Hunter Biden, including those who disseminated or highlighted a cache of files with embarrassing information that appears to have come from an abandoned laptop.

Brock has far more political experience than Morris, but he also has a track record of bare-knuckle tactics that have drawn criticism on both sides of the aisle.

Once a self-described “right-wing hit man,” Brock switched sides and became an ardent supporter of Hillary Rodham Clinton, setting up a political action committee that coordinated with her 2016 presidential campaign to defend her against media scrutiny and attacks from rivals.

Over the past two decades, Brock built a network of nonprofit groups that are supported by some of the biggest donors on the left and that play important roles in the Democratic Party’s ecosystem.

Brock is stepping away from his position as chair of two of his main groups, Media Matters and American Bridge, to focus on Facts First USA, for which he will serve as president. He left open the door to Facts First coordinating with the White House, the Democratic National Committee or other Democratic groups, including a potential Biden campaign if the president declared his candidacy for reelection.

“We’re an outside independent group,” Brock said, “and we hope that lots of people are willing to join the fight against Republican disinformation and conspiracy mongering, including the White House and all allied groups.”