WASHINGTON — President Biden and Speaker McCarthy reached an “agreement in principle” late Saturday as they raced to strike a deal that to limit federal spending and resolve the looming debt crisis ahead of a June 5 deadline, a person familiar with the situation said. A deal would avert a default on the federal government’s obligations.

The Democratic president and Republican speaker reached the agreement after the two spoke earlier Saturday evening by phone, said the person, who was speaking on condition of anonymity because the official was not authorized to speak publicly on the matter. The country and the world have been watching and waiting for a resolution to political standoff that threatened the global economy.

With the outlines of a deal in place, the legislative package could be drafted and shared with lawmakers in time for votes early next week in the House and later in the Senate.

Mr. Biden also spoke earlier in the day with Democratic leaders in Congress to discuss the status of the talks, according to three people familiar with the situation, who spoke on condition of anonymity because they were not authorized to discuss the matter publicly.

“Big, thorny issues remain,” one of the top negotiators, Congressman Patrick McHenry told reporters earlier in the evening.

Some of those outstanding issues, Mr. McHenry said then, “the president and speaker have to resolve at that level.”

Failure to lift the borrowing limit, now roughly $31 trillion, to pay the nation’s incurred bills, would send shockwaves through the economy. Secretary Yellen said failure to act by the new date would “cause severe hardship to American families, harm our global leadership position and raise questions about our ability to defend our national security interests.”

Anxious retirees and others were already making contingency plans for missed checks, with the next Social Security payments due next week.

Lawmakers are not expected to return to work from the Memorial Day weekend before Tuesday, at the earliest, and McCarthy has promised lawmakers he will abide by the rule to post any bill for 72 hours before voting.

The Democratic-held Senate has largely stayed out of the negotiations, leaving the talks to Messrs. Biden and McCarthy. The Senate majority leader, Charles “Chuck” Schumer has pledged to move quickly to send a compromise package to Mr. Biden’s desk.

Weeks of talks failed to produce a deal in part because the Biden administration resisted for months on negotiating with Mr. McCarthy, arguing that the country’s full faith and credit should not be used as leverage to extract other partisan priorities.