As the midnight deadline approached, efforts to finish a deal intensified, and Mr. Obama and Mr. Boehner spoke by telephone to try to find an agreement.

“Both sides are working hard to reach the kind of resolution Americans desire,” said Senator Mitch McConnell of Kentucky, the Senate Republican leader, who had consulted closely with Mr. Boehner on strategy during the fractious talks. “A resolution is actually within reach. The contours of a final agreement are coming into focus.”

Mr. McConnell’s optimism could not disguise the fact that time was steadily slipping away, and testy leaders of the two parties were pushing hard to shape public perceptions of who was responsible for an impasse that threatened to have serious political repercussions — and to presage even more consequential fiscal showdowns in the months ahead. Democrats said Republicans were insisting on overreaching policy provisions; Republicans said it remained about money.

After nightlong negotiations that ended before dawn on Friday yielded no agreement, Senator Reid went on the offensive. He told reporters and said on the Senate floor that Mr. Boehner, the Senate Democrats and Mr. Obama had essentially settled on $38 billion in cuts from current spending, a figure that represented a substantial concession for Democrats.

But he said that Republicans were refusing to abandon a policy provision that would withhold federal financing for family planning and other health services for poor women from Planned Parenthood and other providers.

“This is indefensible, and everyone should be outraged,” Mr. Reid said on the Senate floor. “The Republican House leadership have only a couple of hours to look in the mirror, snap out of it and realize how truly shameful they have been.”

In a terse statement of his own to reporters, Mr. Boehner said there was “only one reason we do not have an agreement yet, and that is spending.” He asked, “When will the White House and when will Senate Democrats get serious about cutting spending?”