Fresh off a resounding midterm elections victory, House Democrats on Sunday began detailing plans to wield their newfound oversight power in the next Congress, setting their sights on acting attorney general Matthew G. Whitaker while rebuffing calls from some liberals to pursue impeachment proceedings against President Trump.

Rep. Jerrold Nadler (D-N.Y.), who is poised to take control of the House Judiciary Committee, said he will call Whitaker as a first witness to testify about his “expressed hostility” to special counsel Robert S. Mueller III’s Russia investigation. Nadler said he is prepared to subpoena Whitaker if necessary.

Another incoming chairman, Rep. Adam B. Schiff (D-Calif.) of the House Intelligence Committee, raised the possibility of investigating whether Trump used “instruments of state power” in an effort to punish companies associated with news outlets that have reported critically on him, including CNN and The Washington Post.

And Democrats on the House Oversight Committee plan to expand their efforts to investigate Trump’s involvement in payments to women who alleged affairs with him before the 2016 election, a committee aide said Sunday night, potentially opening up the president’s finances to further scrutiny.

The moves signal that House Democrats, while wary of the risks of alienating voters who backed the president, are fully embracing their midterm victory last week as a mandate to dig deep into the actions of the executive branch.

“The key lesson that we’ve learned from this last election is that the American people are sick and tired of the Trump administration, and they are looking for a Congress that is going to put a check on the executive branch,” said Democratic strategist Zac Petkanas, a former senior aide to Hillary Clinton’s 2016 campaign.

“Some talk about a backlash against the Democrats, but it was a backlash that brought them into power,” he added. “So, I don’t think they will easily be able to be seen as overreaching by the American people.”

Democrats have a long list of legislative items on their agenda for the next Congress. They include long-sought legislation on gun control, as well as a potential overhaul of the federal Higher Education Act and a vote on protecting health coverage for people with preexisting conditions — an issue that many Democrats successfully wielded against their Republican opponents in last week’s midterms.

But investigations are likely to capture the greatest attention on both ends of Pennsylvania Avenue.

At a news conference last Wednesday, Trump laid down a marker for congressional Democrats, warning them that any investigations into his administration would lead to a “warlike posture” that would threaten the prospects of any bipartisan cooperation.

Democrats have previously said they plan to launch investigations into matters ranging from Trump’s tax returns to his administration’s policies on health care, education and immigration.

On Sunday, Schiff added a new possibility to the mix. The incoming House Intelligence Committee chairman pointed to Trump’s effort to block AT&T from purchasing Time Warner, the parent company of CNN, and his desire to get the U.S. Post Office to increase shipping costs on Amazon.com as potential retaliation against two news outlets the president often complains treats him unfairly. Amazon founder and CEO Jeffrey P. Bezos owns The Post.

“The president is not only castigating the press, but might be secretly using instruments of state power to punish them. That’s a great threat to press freedom,” Schiff said in an interview with The Post. He first brought up the potential investigation during an interview with Axios.

Such a probe would not go through Schiff’s committee, but probably the Oversight or Judiciary panels. Schiff said Democrats are convening when they return to Washington this week and he intends to raise it as a priority with his colleagues.

In an interview on Fox News Channel’s “Sunday Morning Futures,” House Majority Leader Kevin McCarthy (R-Calif.) dismissed Democratic plans to investigate the administration.

“Well, I don’t think the Democrats are going to be able to stop this agenda, because look at how much we have been able to grow,” McCarthy said. “I know what the Democrats want to do, just investigations and impeachment. But as I have said before, America’s too great for a vision so small.”

Rep. Elijah E. Cummings (D-Md.), who is set to become chairman of the House Oversight Committee, sent a letter last month to the White House and the Trump Organization requesting documents related to the hush payments. The documents were not provided at the time, but “this should change now that we are in the majority,” a Democratic committee aide said Sunday night. News of the panel’s plans was first reported by the Wall Street Journal.

The pressure among the Democratic base to move against Trump remains strong: A Washington Post-Schar School poll released last week showed that among voters who supported Democratic House candidates in battleground districts, 64 percent believe Congress should begin impeachment proceedings against the president.

But party leaders have urged calm, emphasizing that before any serious talk of impeachment, a host of investigations — including Mueller’s probe into Russian interference in the 2016 campaign — must first be allowed to bear fruit. They also note that a vote to convict requires a two-thirds vote of the Senate, which will remain in Republican hands.

“We are not doing any investigation for a political purpose, but to seek the truth,” House Minority Leader Nancy Pelosi (D-Calif.) said in an interview with CBS’s “Face the Nation” that aired Sunday.

Pelosi, who is seeking to reclaim the speaker’s gavel in the new Congress, described House Democrats as “very strategic” and “not scattershot” and said that her party will be pursuing “a more open Congress with accountability to the public.” Lawmakers will be “seeking bipartisanship where we can find it” and will “stand our ground where we can’t,” she added.

Democrats appear to be focusing their energy on protecting Mueller’s investigation, which some hope may eventually reveal enough about the president to help sway public opinion in their favor and give them enough fodder to launch proceedings against him.

Trump has repeatedly sought to discredit the Mueller probe, denouncing it as a “witch hunt” and arguing that it should have concluded long ago. His ouster of Jeff Sessions as attorney general last week and appointment of Whitaker over Deputy Attorney General Rod J. Rosenstein to supervise the investigation triggered an outcry among Democrats and other critics, who viewed it as a first step toward the possible scuttling of the probe.

Those fears were exacerbated in recent days amid revelations that Whitaker has been openly critical of the Mueller investigation, including in an appearance on CNN in which he floated the notion of a successor to Sessions who “just reduces [Mueller’s] budget to so low that his investigation grinds to almost a halt.”

“The Republicans in Congress have refused to have any checks to perform our constitutional duty, being a check and balance on the president,” Nadler said in an appearance on CNN’s “State of the Union.” “We will do that. And this is the first step in doing that. The president may think that he is above the law. He may think that he will not be held accountable, but he will be.”

Nadler echoed other top Democrats who say they should hold their fire on the question of impeachment until they know what Mueller has uncovered. His test, he said, is whether there’s enough evidence to convince even Trump supporters that such a step is necessary.

“Is the evidence so strong . . . [that] when all this is laid out publicly, a very large fraction of the people who voted for the president will grudgingly acknowledge to themselves and to others that you had no choice but to impeach the president?” Nadler said.

Democrats in the Senate will also be pushing for legislation to prevent Whitaker from interfering with the Mueller investigation and will seek to attach it to a must-pass spending bill, Minority Leader Charles E. Schumer (D-N.Y.) said Sunday.

“There’s no reason we shouldn’t add this and avoid a constitutional crisis,” Schumer said on CNN. But he demurred when asked if Democrats would shut down the government over it, and said House Democrats should await the Mueller report before considering impeachment.

Trump will probably nominate a permanent attorney general “early next year,” one of his top congressional allies, Sen. Lindsey O. Graham (R-S.C.), said Sunday on CBS’s “Face the Nation.”

That means that the battle over Whitaker’s role in the Mueller investigation could be largely finished by the time Democrats assume control of the House in January, said Orin Kerr, a law professor at the University of Southern California. The greatest tool at Democrats’ disposal will then be their fact-finding ability, he said.

“The key question is, what can we learn about what the executive branch has been doing?” Kerr said. “That matters more than impeachment, given that we won’t get removal from the Senate Republicans.”

Stephen Spaulding, director of strategy at the nonprofit watchdog group Common Cause, said that there is a “real pent-up need for oversight” and that Democrats now have an obligation to do the work that outside organizations have largely been doing over the past two years through actions such as Freedom of Information Act requests.

“It’s about following the evidence, asking tough questions,” Spaulding said. “It truly is about accountability. We’ve had two years with one party controlling both houses of Congress and, in some cases, actively undermining investigations. There’s a backlog of answers; at the same time, there has to be a smart and strategic approach.”