WASHINGTON (AP) — President Barack Obama and House Speaker John Boehner searched on Friday for an elusive debt-limit compromise as the Senate rejected a House plan containing deep spending cuts and for the moment put aside a last-ditch fallback option.

The 51-46 party-line Senate vote, and a decision by Senate Majority Leader Harry Reid, D-Nev., to cancel weekend Senate sessions, left unresolved the urgent issue of how to lift the nation's borrowing powers to avoid a first-ever U.S. default on Aug. 3.

The moves also cleared the way for private negotiations between the president, Boehner and other key players.

But neither the president nor the speaker was openly optimistic that they would succeed.

Boehner, R-Ohio, told reporters that, despite reports that Obama and he were closing in on a $3 trillion deficit-reduction deal, "There was no agreement, publicly, privately, never an agreement, and frankly not close to an agreement."

"So I suggest it's going to be a hot weekend here in Washington, D.C.," he added.

Obama urged congressional factions to unite and suggested the biggest obstacle to a deal remains a bloc of conservative Republicans in the House.

He said at a town hall-style meeting at the University of Maryland in College Park, Md., that he was still open to a deal — even if it means deeper domestic spending cuts than many in his own party can stomach.

"I am willing to sign a plan that would include tough choices I would not ordinarily sign," he said. "Whether I like it or not, I've got to get the debt ceiling raised."

He made no mention of whether he believed progress was being made in his negotiations with Boehner.

The president also for the first time dismissed a strategy promoted by some liberals as a possible solution, the notion that the 14th Amendment to the Constitution might give the president the ability to proceed unilaterally in raising the debt limit without congressional approval.

"I have talked to my lawyers, they are not persuaded that that is a winning argument," he said.

The administration says the government is in danger of defaulting for the first time in its history after an Aug. 2 deadline, unless Congress raises the $14.3 trillion federal debt ceiling so the U.S. can keep borrowing enough to pay its bills.

Those in both parties want to couple a deficit-reduction provision to the debt limit increase. Obama and his Democratic allies want the package to include some tax increases while Republicans want to do it with spending cuts alone.

The vote in the Democratic-controlled Senate blocked a House-passed bill, strongly backed by tea party factions, that would have required Congress to slash spending and pass a balanced budget amendment before raising the nation's borrowing powers.

The House measure was a GOP conservative priority, although its passage in the Democratic-controlled Senate was never expected. Still, the narrow party line vote underscored the deep differences between the two parties on deficit reduction.

Boehner, in a speech on the House floor following the Senate vote, said, "The House has acted. ...We've done our job. The Democrats who run Washington have done nothing. They can't stop spending the American people's money. They won't and they refuse."

After the vote, Reid said the Senate would not meet over the weekend and that he was temporarily putting aside a backup plan he had been pushing along with Senate Republican Leader Mitch McConnell of Kentucky.

That plan would guarantee that the president would get a debt ceiling increase through 2012. But it would extract a political price from Obama, who would have to ask Congress for increases in three separate increments, and it would allow Republicans to avoid casting a difficult vote in favor of a debt ceiling increase that would anger their constituents.

"Circumstances have changed. The speaker of the House and the president have been working to reach agreement on a major deficit-reduction measure. I wish them both very well," Reid said in a floor speech.

Reid said that talks ongoing between Obama and Boehner are focused on producing legislation involving taxes and that the House would have to act before the Senate, because tax measures must originate in the House.

Sen. Kent Conrad, D-N.D., a member of a group of senators known as the Gang of Six who proposed a plan to cut the deficit by about $4 trillion over ten years, with $1 trillion coming from taxes, suggested various options may still be in play.

"I don't think anybody can be certain at this moment what the outcome will be," he said.

Meanwhile, Treasury Secretary Timothy Geithner, Federal Reserve Chairman Ben Bernanke and New York Fed President William Dudley met Friday morning "to discuss the implications for the U.S. economy if Congress fails to act," they said in a joint statement. But the statement said they "remain confident that Congress will raise the debt ceiling soon."

Separately, former Treasury Secretary Henry Paulson, who served under President George W. Bush, had a breakfast meeting with Geithner and said afterward, "Failing to raise the debt ceiling would do irreparable harm to our credit standing, would undermine our ability to lead on global economic issues and would damage our economy."

Boehner underscored his willingness to keep negotiations going, telling reporters, "As a responsible leader, I think it is my job to keep lines of communications open."

The continuing Obama-Boehner talks kept alive the possibility of substantial deficit reduction that would combine cuts in spending on major benefit programs like Medicare and Medicaid and revenue increases through a broad overhaul of the tax code.

At the University of Maryland, Obama told his audience of mostly students that, "The United States of America doesn't run out without paying the tab. We pay our bills. We meet our obligations."

Asserting that the American people as well as many in Congress are on board with his approach of mixing higher taxes for some with steep spending cuts, the president said, "The only people we have left to convince are some folks in the House of Representatives and we're going to keep working on that."

White House spokesman Jay Carney said Thursday that Obama remained "unalterably opposed" to debt limit extensions in the order of six months, nine months or one year. "His premise is that we have to raise the debt ceiling for an extended period of time into 2013 regardless," Carney said.

Democratic officials familiar with the Obama-Boehner discussions said both sides remained apart on key components of the deal, including the amount of revenue that a revamped tax code could yield, the nature of the changes to Medicare and Medicaid, and the process that would guarantee that both taxes and benefit programs would in fact be overhauled.

Republicans have insisted that entitlement programs such as Medicare need substantial changes, but have loudly objected to any revenue provision that could be deemed a tax increase. Democrats, eager to keep changes to their cherished health care programs to a minimum, have demanded that any plan must have new tax revenue.

Democrats in the Senate reacted angrily when word spread that Obama and the House leaders appeared to be closing in on a deal that would include $3 trillion in spending cuts but only a promise of higher revenues to be realized through a comprehensive overhaul of the tax code.

White House officials went out of their way to deny that a deal was near.