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The 64-to-34 vote ended for now a showdown that had threatened the full faith and credit of the United States government. The Treasury Department has been shuffling federal accounts for a month to make sure it could pay interest to its creditors even after the government officially breached its borrowing limit. By mid-February, the Obama administration warned, the Treasury would have exhausted such "extraordinary measures" and would have been forced to default for the first time.

The deal "sets an important precedent," said Senator Harry Reid of Nevada, the majority leader, "that the full faith and credit of the United States will no longer be used as a pawn to extract painful cuts to Medicare, Social Security or other initiatives that benefit the middle class. A clean debt ceiling increase that allows the United States to meet its existing obligations should be the standard."

The legislation, written by House Republican leaders, passed the House last week 285 to 144, with most Republicans voting for it. In the Senate, most Republicans — and Senator Joe Manchin III, Democrat of West Virginia — voted no.

Mr. Reid's hope for an end to such showdowns on the debt ceiling may prove to be optimistic. The next budget fight will come March 1, when across-the-board military and domestic spending cuts totaling $1 trillion over 10 years would begin to go into force. House Republicans say they would entertain proposals to shift those cuts to other programs but will not back down on the spending reduction.

On March 27, the current stopgap law financing the government will expire, raising the specter of an Easter government shutdown. Then on May 18, the debt ceiling will come back into force unless a broader deficit reduction deal can be reached before then.

"We're going to be back here in a few months with the same impasse," said Senator Patrick Toomey, Republican of Pennsylvania.

The final vote on the debt limit deal came only after Mr. Reid and Senator Mitch McConnell of Kentucky, the Republican leader, reached agreement on an orchestrated path to passage. To get there, the Senate voted on four Republican amendments. One would have added spending cuts to the deal. One would have mandated that in the event of a debt ceiling impasse, the Treasury would wall off incoming tax receipts to pay interest on the federal debt, Social Security benefits, and active military pay.

Senator Max Baucus of Montana, chairman of the Finance Committee, compared that to "The Hunger Games," saying it would pit all other federal programs against one another, just as the fictional games pitted children against children in a fight to the death.

"It'd be total chaos," he said.

Senator Rand Paul, Republican of Kentucky, was given a vote to stop the sale of F-16 fighter jets and Abrams tanks to Egypt, the most recent of a series of votes Mr. Paul has forced to cut off aid to Egypt in the wake of the rise of the Muslim Brotherhood. Senators of both parties said the amendment would cut off all military assistance and end American leverage in Egypt.

Under the Reid-McConnell agreement, all of those amendments would have required 60 votes, and all failed by design.

Mr. McConnell expressed Republican hopes that passage would begin tough but fruitful negotiations on the deficit that would include proposals to control the growth of entitlement programs like Social Security and Medicare, which are being propelled by an aging population.

"The president and his allies have had four years to put their ideas into practice. Those policies have failed," Mr. McConnell said. "It's time for a new approach. And, if Democrats are ready to finally get serious — to end the blame game and pursue real pro-growth policies — then Republicans are here to show them the way forward."