Nearly two years ago, Democrats could do little more than watch as President Trump seized control of the U.S. budget, slashing billions of dollars and firing droves of civil workers in a downsizing that Congress never authorized.

Now, as the party prepares to take charge in the House and Senate, its incoming leaders say they are plotting ways to keep Mr. Trump in check.

In the wake of their overwhelming electoral victory, Democrats have promised to cement their power under the Constitution to control the nation’s purse. They hope to boost funding for federal climate, education, health, housing and safety net initiatives next year, then take steps that would prevent Mr. Trump from slowing down or interfering with the money again.

Many of these programs have experienced steep cuts and disruptions during Mr. Trump’s second term, as the White House embraces an expansive view of its power to override Congress. Even though lawmakers have approved the money, Mr. Trump has often refused to spend it or has used the funds for other purposes, drawing rebukes in court — and, on rare occasion, from some Republicans.

Democrats also plan to investigate the architect of that strategy: Russell T. Vought, the White House budget chief who has been working on a “fiscal consolidation” plan that could involve additional cuts, according to other officials.

Over the past two years, Mr. Vought has frequently tried to rebuff congressional oversight of his budget activities. And the White House on Thursday appeared to be considering one of Mr. Vought’s deputies for a post whose responsibilities include monitoring the budget office’s handling of federal spending.

“We’re going to ask Russ Vought a lot of questions,” said Senator Patty Murray of Washington, the top Democrat on the Appropriations Committee, adding that Congress would reassert its authorities and aim to “Trump-proof” its spending bills.

The plans reflect a broader reckoning on Capitol Hill, where the outgoing Republican majority had largely acquiesced to the Trump administration’s whims. But for Democrats, the task still may not be easy: Even with healthy margins in the House and Senate, they still would require some G.O.P. support to override a veto from Mr. Trump.

“I know there are people who are interested in these areas and want to reclaim the power of the purse,” said Representative Rosa DeLauro of Connecticut, the senior Democrat on the House Appropriations Committee.

Ms. DeLauro added that she was hopeful Democrats would be able to work with Republicans. But she also made clear that Democrats would seek to curtail Mr. Trump in other ways, if necessary, even if it meant Congress taking legal action against the administration.

“We can go to the courts,” she said, adding that the party would “look for every conceivable tool to thwart their efforts.”

For Mr. Trump, the roughly $2 trillion approved annually by Congress has become a political cudgel. He and his aides have adopted the view that they have immense power to reprogram federal spending as they see fit, triggering countless lawsuits that have often found that the administration broke the law.

Over the past two years, the president has frequently moved around money to accomplish his personal goals, whether it is to fund the construction of his White House ballroom or to pay immigration agents during a federal shutdown. He has also struck entire categories of spending — in science, education and foreign aid — simply because funding programs and their recipients were not aligned with his political views.

At one point, the White House proposed subjecting nearly every federal grant to a political litmus test, an idea that proved so objectionable that Republicans later joined Democrats to block it. And the administration has repeatedly weaponized the budget to deny federal aid to Democrats, a threat that Mr. Trump repeated on Thursday.

At the center of that strategy is Mr. Vought, who reprised his role as the leader of the Office of Management and Budget with the goal of slashing spending seen as “woke,” merging socially conservative values and the perennial Republican interest in austerity.

The president’s budgets, prepared by Mr. Vought, have twice called on Congress to make drastic cuts across most domestic programs, especially in science and those that aid the poor. In both cases, lawmakers rejected the White House blueprints, only to see Mr. Vought try to carry out some of the cuts on his own.

The White House did not respond to a request for comment. Mr. Vought has argued for years that he is acting within the law.

Daniel Kowalski, a former O.M.B. official in the Trump administration who now directs a budget center for the right-leaning Heritage Foundation, said he expected that pattern to continue even as Democrats prepared to assume their new majorities.

“I think there’s going to be a little bit of a cat-and-mouse game,” said Mr. Kowalski. “The Democrats are going to try to limit, and the administration is going to try to work around.”

That was evident within days of the election. In a pair of interviews, the two Democrats overseeing the annual appropriations process said that they had a number of such limits in mind.

Ms. DeLauro and Ms. Murray each said they would leverage their power over funding to fight what they described as Mr. Trump’s corruption, while aiming to restrict his policies, particularly his ability to carry out the war with Iran.

The two Democrats said they were especially interested in protecting the National Institutes of Health and the Centers for Disease Control and Prevention, whose grants face strict political scrutiny in the Trump administration.

Democrats also hope to make it harder for the administration to cut or transfer spending without congressional permission. That includes closing off a loophole that allowed Mr. Vought to hold up billions of dollars in health, education and foreign aid at the end of the last two fiscal years, effectively causing the funds to expire, even though lawmakers never agreed to such a cut.

The tactic is known as a pocket rescission, and Mr. Vought insists it is legal. The White House budget chief has also supported the idea that the president can refuse to spend appropriated money altogether, a move known as impoundment, which is illegal.

Democrats said they planned to toughen up those restrictions on impoundment, and Ms. Murray said the party would couple its new rules with unspecified “penalties for breaking our laws” on spending.

The new strictures on the president would build on the more limited reforms that Democrats worked with Republicans to enact over the past year. The technical changes generally sought to force the White House to spend the amounts that Congress had dictated on paper.

Republicans otherwise had resisted more serious constraints on the president’s budgetary powers, and the White House largely shrugged off the rules, prompting another round of court battles. But the moment illustrated the growing, bipartisan discord with Mr. Vought.

The outrage has hardly deterred the White House.

As soon as this week, the president is expected to nominate a new comptroller general who would lead the Government Accountability Office, a congressional watchdog that is responsible for overseeing the administration’s handling of federal spending. It carries a 15-year term, replacing Gene Dodaro, who retired when his term expired at the end of last year.

The administration has eyed Eric Ueland, a top O.M.B. official, to take the post, according to two people familiar with the matter, who spoke on condition of anonymity to discuss plans that were not finalized. If the president proceeds, and the Senate confirms him, it would put in place an ally of Mr. Vought’s in a role that helps to oversee the budget director.

The Washington Sun previously reported on the possible nomination.

In an unorthodox move, Republicans this week raced to start the nomination process before they had formally received a nominee. The Senate Homeland Security and Governmental Affairs Committee merely listed the position — without a name — for an initial hearing on Nov. 19.

A spokesman for Senator Rand Paul of Kentucky, the Republican chairman of the panel, did not respond to a request for comment. The move angered Democratic leaders, including Senator Chuck Schumer and Representative Hakeem Jeffries, both of New York, who in a joint statement criticized Mr. Trump for trying to “install a fox in the henhouse.”

“I absolutely expect that O.M.B. will continue to abuse its authority to withhold funds for the programs the administration disfavors,” said Cerin Lindgrensavage, who serves as a counsel at Protect Democracy, a group that has repeatedly, and successfully, sued the administration over its budget tactics.

Ms. Lindgrensavage said she would “expect that problem to get worse and not better until Congress creates real consequences for O.M.B.”