ap photo Speaker of the House Kevin McCarthy, R-Calif., holds an event to mark 100 days of the Republican majority in the House, at the Capitol in Washington, Monday. In a speech Monday at the New York Stock Exchange, the Republican leader accused President Joe Biden of refusing to engage in budget-cutting negotiations to prevent a debt crisis.

WASHINGTON — House Speaker Kevin McCarthy worked furiously Tuesday to build support for a Republican plan that would demand strict limits to federal spending in return for agreeing to raise the nation’s debt limit and stave off an unprecedented U.S. default.

But President Joe Biden swiftly swatted down the plan, which would cap much federal spending at increases of 1% a year, as requiring “huge cuts” to programs helping millions of Americans.

It was just the latest in what is expected to be a protracted debate over how, when and even whether to raise the nation’s debt limit, now at $31 trillion, with default and a potentially devastating blow to the economy possible if Congress fails to act.

McCarthy is finding unusual support for his plan from his typically fractured House Republican majority, who view the proposal as a calling card to push Biden into negotiations. The White House has so far refused to engage in debt ceiling talks, doubtful McCarthy can unify Republicans and steer any proposal to passage.

Biden, in his first public remarks on the proposal, said at the White House that McCarthy had effectively proposed “huge cuts to important programs” that millions of U.S. households depend on.

The president said that McCarthy has “threatened to be the first one to default on the debt, which would throw us into a gigantic recession and beyond unless he gets what he wants in the budget.”

The high-stakes battle comes as Biden confronts this year’s newly divided government with Republicans in charge of the House and eager to flex their majority power.

If McCarthy succeeds in having the House pass his proposal, he would be able to enter into spending talks with the White House showing that he has the backing of his fellow GOP lawmakers. Biden says the Republicans should first reveal their own detailed spending plan — free of any connection to the debt limit. And administration officials have privately expressed doubts about the benefits of negotiating with McCarthy out of skepticism that he can actually deliver conservative Republican votes.

Democratic Minority Leader Hakeem Jeffries quipped on CNBC that the House Republicans’ budget plan is “in the witness protection program.”

McCarthy, unable to pass a comprehensive Republican budget plan in the House, instead has been working with his leadership team to unite the “five families” — the often warring factions of Republican caucuses — to join together on his new, more general plan. He convened lawmakers Tuesday for a private meeting to discuss the proposal.

“I’m confident we’ll have it and comfortable we’ll pass it,” said Rep. Tom Cole, R-Okla., chairman of the Rules Committee, who said a bill could come up for a vote as soon as next week.

Even some of McCarthy’s skeptics from the staunchly conservative House Freedom Caucus — including those who initially refused to back him to be speaker — seemed ready to give his debt ceiling proposal a look. But others remained deeply skeptical, as they started piling on their own conservative priorities, showing the limits of the speaker’s grip on his majority.