WASHINGTON — With days to spare before a potential government default, President Biden and Speaker McCarthy reached final agreement Sunday on a deal to raise the nation’s debt ceiling and worked to ensure enough support in Congress to pass the measure in the coming week.

The Democratic president and Republican speaker spoke late in the day as negotiators rushed to draft and post the bill text for review, with compromises that neither the hard-right or left flank is likely to support. 

Instead, the leaders are working to gather backing from the political middle as Congress hurries toward votes before a June 5 deadline to avert a damaging federal default.

“Good news,” Mr. Biden declared Sunday evening at the White House.

“The agreement prevents the worst possible crisis, a default, for the first time in our nation’s history,” he said. “Takes the threat of a catastrophic default off the table.”

The president urged both parties in Congress to come together for swift passage. “The speaker and I made clear from the start that the only way forward was a bipartisan agreement,” he said.

The final product includes spending cuts but risks angering some lawmakers as they take a closer look at the concessions. Mr. Biden told reporters at the White House upon his return from Delaware that he was confident the plan will make it to his desk.

Mr. McCarthy, too, was confident in remarks at the Capitol: “At the end of the day, people can look together to be able to pass this.”

The days ahead will determine whether Washington is again able to narrowly avoid a default on U.S. debt, as it has done many times before, or whether the global economy enters a potential crisis.

In the United States, a default could cause financial markets to freeze up and spark an international financial crisis. It would all but shatter the $24 trillion market for Treasury debt.

Anxious retirees and others were already making contingency plans for missed checks, with the next Social Security payments due soon as the world watches American leadership at stake.

Mr. McCarthy and his negotiators portrayed the deal as delivering for Republicans though it fell well short of the sweeping spending cuts they sought. Top White House officials were briefing Democratic lawmakers and phoning some directly to try to shore up support.

One surprise was a provision important to the influential West Virginia Democrat, Senator Manchin, giving congressional backing for the Mountain Valley Pipeline, a natural gas project, that is certain to raise questions.

Negotiators also agreed to some Republican demands for increased work requirements for food stamps recipients that Democrats had called a nonstarter.

Mr. McCarthy told reporters at the Capitol on Sunday that the agreement “doesn’t get everything everybody wanted,” but that was to be expected in a divided government. Privately, he told lawmakers on a conference call that Democrats “got nothing.”

Weeks of negotiations came together when Messrs. Biden and McCarthy spoke by phone Saturday evening and agreed in principle to the deal, finishing it up Sunday with the 99-page legislative text made public.

Support from both parties will be needed to win congressional approval before the projected June 5 government default on America’s debts. Lawmakers are expected to return Tuesday from the Memorial Day weekend, and Mr. McCarthy has promised lawmakers he will abide by the rule to post any bill for 72 hours before voting in the House, as soon as Wednesday.

The package would next go to the Senate, where the Republican leader, Senator McConnell, said senators “must act swiftly and pass this agreement without unnecessary delay.”

Central to the compromise is a two-year budget deal that would essentially hold spending flat for 2024, while boosting it for defense and veterans, and capping increases at 1 percent for 2025. That’s alongside raising the debt limit for two years, pushing the volatile political issue past the next presidential election.

Driving hard to impose tougher work requirements on government aid recipients, Republicans achieved some of what they wanted. It ensures people ages 49 to 54 with food stamp aid would have to meet work requirements if they are able-bodied and without dependents. Mr. Biden was able to secure waivers for veterans and homeless people.

The deal puts in place changes in the landmark National Environmental Policy Act designating “a single lead agency” to develop environmental reviews, in hopes of streamlining the process.

It halts some funds to hire new Internal Revenue Service agents as Republicans demanded, and rescinds some $30 billion for coronavirus relief, keeping $5 billion for developing the next generation of Covid vaccines.

The deal would suspend the debt limit until January 2025. It came together after Secretary Yellen told Congress that the United States could default on its debt obligations by June 5 — four days later than previously estimated. Lifting the nation’s debt limit, now at $31 trillion, allows more borrowing to pay bills already incurred.

Mr. McCarthy commands only a slim Republican majority in the House, where hard-right conservatives may resist any deal as insufficient as they try to slash spending. By compromising with Democrats, he risks angering his own members, setting up a career-challenging moment for the new speaker.

“I think you’re going to get a majority of Republicans voting for this bill,” Mr. McCarthy said on “Fox News Sunday,” adding that because Mr. Biden backed it, “I think there’s going to be a lot of Democrats that will vote for it, too.”

The House Democratic leader, Congressman Hakeem Jeffries of New York, said on CBS’ “Face the Nation” that he expected there will be Democratic support but he declined to provide a number. Asked whether he could guarantee there would not be a default, he said, “Yes.”

A 100-strong group of moderates in the New Democratic Coalition gave a crucial nod of support Sunday, saying in a statement it was confident that Mr. Biden and his team “delivered a viable, bipartisan solution to end this crisis.”

The coalition could provide enough support for Mr. McCarthy to make up for members in the right flank of his party who have expressed opposition before the bill’s wording was even released.

It also takes pressure off Mr. Biden, facing criticism from progressives for giving into what they call hostage-taking by Republicans.

Congresswoman Pramila Jayapal of Washington state, who leads the Congressional Progressive Caucus, told CBS that the White House and Mr. Jeffries should worry about whether caucus members will support the agreement.