Senators voted 51 to 46 along party lines to set aside the measure, known as the “cut, cap and balance” bill, which was sent to the Senate by the House this week and seen by conservative House members as their preferred option for increasing the debt ceiling. For many House Republicans, the legislation was their best offer in the continuing standoff with President Obama and Congressional Democrats.

  After the vote, Senator Harry Reid, the Nevada Democrat and majority leader, said the Senate was for the moment abandoning its  fallback plan and would not  immediately move ahead with a procedural maneuver proposed by Senator Mitch McConnell of Kentucky to increase the debt limit. He said the Senate would instead await the results of negotiations between Mr. Obama and the House speaker, John A. Boehner of Ohio, over a broad deficit reduction package.

  “The path to avert default now runs through the House of Representatives,” Mr. Reid said after Democrats voted against the House plan.  He said that he was canceling plans to keep the Senate in session over the weekend and that lawmakers would instead reconvene Monday, just more than a week before the Aug. 2 deadline set by the Treasury Department for increasing the $14.3 trillion limit.

  The debt fight was turning into what Senator Mark Pryor, Democrat of Arkansas, described as a “cliffhanger moment,” with no resolution in sight even as talks continued  between the president and the speaker.

Mr. Obama said at a town hall meeting where he was taking questions Friday morning that he was willing to agree to “historic” spending cuts in an effort to trim the nation’s budget deficit, and urged Congressional factions to come together and reach a deal. He said it was not conceivable that the United States would default on its debt.

“This is a rare opportunity for both parties to come together and choose a path where we stop putting so much debt on our credit card,” Mr. Obama said. 

But he repeated his demand that spending cuts be accompanied by revenue increases, and said tackling the rising costs of Medicare and Medicaid was necessary in order to preserve those programs.

Before a friendly audience, he spoke, sometimes in stark terms, of the concessions that Democrats will have to make in order to get the budget deal passed.

“I’ve agreed to also target some programs that I actually think are worthwhile,” the president said. “They’re cuts that some people in my own party aren’t too happy about. And frankly, I wouldn’t make them if money weren’t so tight.”

Even before he has reached a sweeping budget and debt deal with Mr. Boehner, Mr. Obama is trying to sell his concessions to Congressional Democrats, many of whom fear a “grand bargain” will undercut their party’s ability in the 2012 campaigns to use Republicans support of deep cuts in Medicare, Medicaid and Social Security against them.

On the campus of the University of Maryland in College Park, Mr. Obama thrust himself deep into heavily Democratic country — there were few Republicans to be found among the audience of around 2,500 at the town hall meeting in Ritchie Coliseum on Friday. Mr. Obama fielded an array of questions that in many ways showcased the deep mistrust with which some on the left are viewing the budget negotiations.

One man said he had cerebral palsy and needed health services (“Please don’t leave us holding the bag,” he said, to cheers from the audience). Another woman who said she was a teacher asked Mr. Obama how she was supposed to teach her students about compromise when Republicans never did so.

“I’m sympathetic to your view that this would be easier if I could do this on my own,” Mr. Obama said to another man who suggested that Republican demands for deeper cuts be tossed aside. “But that’s not how our democracy works, and Americans made a decision about divided government.”

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 Though the Senate would not be in session, Mr. Reid said meetings would be occurring all weekend to try to resolve the impasse. “I hope this weekend brings good sense, common sense and vitality to the work that is being done in the House of Representatives,” Mr. Reid said.

   Republicans criticized Democrats for their rejection of the House plan.

  “Senate Democrats have defied the will of the American people who overwhelmingly support real spending cuts, caps on future spending and a balanced budget to create a better environment for private-sector job growth,” Mr. Boehner said.

  But the outcome was  a foregone conclusion and leaders of both parties said the Senate needed to dismiss the House plan to show Republicans that the proposal was dead, clearing the way for an alternative, though exactly what that alternative would be was unclear.

Mr. Obama for the first time addressed — and ruled out — the idea that the Constitution empowers a president to increase the debt limit to prevent default and, as he put it, “basically ignore” the federal law requiring that the debt ceiling be set by statute. The argument of “the constitutional option,” which President Bill Clinton — like Mr. Obama a former constitutional law instructor — endorsed in an interview this week, is based on the 14th Amendment’s provision that the validity of the United States debt “shall not be questioned.”

“I have talked to my lawyers,” Mr. Obama said, and “they are not persuaded that that is a winning argument.”

Michael D. Shear and Jackie Calmes contributed reporting.

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