After weeks of negotiations, President Biden and Speaker McCarthy have announced an “agreement in principle” to raise the nation’s debt ceiling and avoid a potentially catastrophic default.

The agreement includes spending cuts demanded by Republicans, but it is short of the reductions in the sweeping legislation passed by the Republican-led House last month.

To reduce spending, as Republicans had insisted, the package includes a two-year budget deal that would hold spending flat for 2024 and impose limits for 2025. That’s in exchange for raising the debt limit for two years, until after the next election.

It also expands some work requirements for food-stamp recipients and tweaks an environmental law to try to streamline reviews to build new energy projects.

Secretary Yellen has said the United States could default on its debt obligations by June 5 if lawmakers do not act in time to raise the federal debt ceiling.

Speaking to reporters in the Capitol late Saturday, Mr. McCarthy said the bill has “historic reductions in spending, consequential reforms that will lift people out of poverty into the workforce and rein in government overreach. There are no new taxes and no new government programs.”

Still, he said, “we still have more work to do tonight to finish all the writing of it.” The speaker and his lead negotiators were still holed up in his office as midnight approached.

Mr. McCarthy said he would speak to Mr. Biden again on Sunday. The House minority leader, Hakeem Jeffries, said in a letter to Democratic colleagues that Messrs. Biden and McCarthy planned to speak by no later than 2 p.m. Sunday to complete the agreement and that Biden administration officials would brief House Democrats on the agreement at 5 p.m.

Mr. Biden said in a statement that “over the next day, our negotiating teams will finalize legislative text and the agreement will go to the United States House and Senate. I strongly urge both chambers to pass the agreement right away.”

The agreement is “an important step forward that reduces spending while protecting critical programs for working people and growing the economy for everyone,” Mr. Biden said.

To pass the bill, both Messrs. McCarthy and Biden will now have to sell it to their respective parties. While both sides are expected to lose some votes, they have to make sure that the deal is popular enough to pass both chambers without a revolt on either side.

Mr. McCarthy held a call Saturday evening with the Republican caucus, fulfilling a promise he made to show the agreement to them before revealing the legislation to the public. He said he expects to release the text of the bill on Sunday afternoon.

Mr. McCarthy said in an interview on “Fox News Sunday” that the bill is less than 150 pages and the House would wait 72 hours before voting on it so it can be publicly reviewed. “This is worthy of the American people. I want them to read it. I want them to understand it,” he said.

The Republican speaker said he expects a majority of Republicans to vote for it and a lot of Democrats as well because Mr. Biden was on board. Mr. Jeffries said on CBS’ “Face the Nation” that he expects “there will be Democratic support once we have the ability to be fully briefed by the White House, but I’m not going to predict what those numbers will ultimately look like.”

Reaction was mixed. Dan Bishop, a Republican congressman from North Carolina, tweeted a vomit emoji, complaining that some Republicans on the call were praising the speaker for getting what he said is “almost zippo in exchange” for the debt ceiling hike.

Dusty Johnson, an ally of McCarthy from South Dakota, told CNN’s “State of the Union” that “overwhelmingly, Republicans in this conference are going to support the deal. How could they not. It’s a fantastic deal.”

White House officials will give their own briefing to House Democrats on Sunday at 5 p.m., according to a House Democratic aide. Mr. McCarthy said he spoke to Senator McConnell on Saturday night and there will be a conference call with Republicans senators later Sunday.

Both the House and Senate are expected to return on Tuesday, after Memorial Day. Mr. McCarthy said the House will vote Wednesday, which would then send the bill to the Senate.

Once the bill reaches the Senate, where Democrats have the majority, the pace of action will largely depend on whether any senators try to hold up the bill, possibly with amendment votes. That could tie up the legislation for a few days.

Still, the Senate can move quickly when they have agreement from all 100 senators. The bill could be passed by the end of the week, with a quick Biden signature to make it law.

If all goes according to Mr. McCarthy’s plan — and both chambers are able to pass the legislation — the potential crisis should be resolved by June 5, which is when the Treasury Department projects the United States would be at risk of default.

“This agreement is good news for the American people, because it prevents what could have been a catastrophic default and would have led to an economic recession, retirement accounts devastated, and millions of jobs lost,” Mr. Biden said in his Saturday evening statement.