President Biden and Speaker Kevin McCarthy on Saturday reached an agreement in principle to lift the debt limit for two years while cutting and capping some government spending over the same period, a breakthrough after a marathon set of crisis talks that has brought the nation within days of its first default in history.

Congressional passage of the plan before June 5, when the Treasury is projected to exhaust its ability to pay its obligations, is not assured, particularly in the House, which plans to consider it on Wednesday. Republicans hold a narrow majority in the chamber, and right-wing lawmakers who had demanded significantly larger budget cuts in exchange for lifting the borrowing limit were already in revolt.

But the compromise, which would effectively freeze federal spending that had been on track to grow, had the blessing of both the Democratic president and the Republican speaker, raising hopes that it could break the fiscal stalemate that has gripped Washington and the nation for weeks, threatening an economic crisis.

Mr. Biden urged the House and Senate to pass the agreement in a late-night statement issued by the White House, saying it would prevent a catastrophic default.

“It is an important step forward that reduces spending while protecting critical programs for working people and growing the economy for everyone,” Mr. Biden said. “And the agreement protects my and congressional Democrats’ key priorities and legislative accomplishments. The agreement represents a compromise, which means not everyone gets what they want.”

The president and Mr. McCarthy spoke by phone on Saturday evening to resolve final sticking points.

In a nighttime news conference outside his Capitol office that lasted just one minute, Mr. McCarthy said the deal contained “historic reductions in spending, consequential reforms that will lift people out of poverty into the work force, rein in government overreach” and would add no new taxes. He declined to answer questions or provide specifics, but said he planned to release legislative text on Sunday.

“We still have more work to do tonight to finish all the writing of it,” he said.

The plan was structured with the aim of enticing votes from both parties, though it has drawn the ire not only of conservative Republicans but also Democrats furious at being asked to vote for cuts they oppose with the threat of default looming.

Still, it gives Republicans the ability to say that they succeeded in reducing some federal spending — even as funding for the military and veterans’ programs would continue to grow — while allowing Democrats to say they spared most domestic programs from significant cuts.

The deal would suspend the borrowing limit, which is currently $31.4 trillion, for two years — enough to get past the next presidential election.

According to a person familiar with the agreement, it also would impose new work requirements for some recipients of government aid, including food stamps and the Temporary Assistance for Needy Families progra