WASHINGTON (AP) -- The Senate on Friday firmly rejected a House Republican bill to slash spending and require a balanced-budget amendment, leaving unresolved with just days to go the urgent issue of increasing the nation's borrowing powers.

The 51-46 Senate vote against the tea party-backed measure - which had been expected in the Democratic-run chamber - came shortly after House Speaker John Boehner told reporters he and President Barack Obama had failed to reach a separate agreement to resolve the debt crisis.

"There was no agreement, publicly, privately, never an agreement, and frankly not close to an agreement," Boehner said. "So I suggest it's going to be a hot weekend here in Washington, D.C."

If progress is to be made over the weekend in the nation's steamy capital, it will have to be made behind closed doors and not in the open.

Senate Majority Leader Harry Reid, D-Nev., canceled planned weekend Senate sessions, increasing the pressure on Obama, Boehner and other top-level negotiators to strike a deal.

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.

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

The administration says the government is in danger of defaulting for the first time in its history after August 2 unless Congress raises the federal debt ceiling so it can keep borrowing enough to pay its bills.

But Democrats and Republicans have been deadlocked over terms of a deficit-reduction package linked to the debt-limit increase, with Democrats demanding some tax increases and Republicans insisting on doing it just with spending cuts.

The focus now is on efforts by Obama and Boehner to come up with an ambitious $4 trillion "grand bargain" that would secure the support of rank-and-file lawmakers. But wide differences still remain.

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.

"We have the opportunity to do something big and meaningful," Obama declared in a newspaper opinion piece. Later Friday, the president took his case to the public again in a town hall-style meeting. Earlier, from the Capitol, Boehner said House Republicans were prepared to compromise and prodded Obama: "The ball continues to be in the president's court."

Even as Republicans contended with the demands of tea party-backed House members, worry was shifting to how to keep Democrats in line if a compromise is reached between Boehner and Obama.

Talk of a deal prompted a spasm of distress among Senate Democrats worried that Obama would agree to immediate cuts but put off steps to increase tax revenues that the president has said are key to any agreement. The White House immediately sought to tamp down talk of an impending deal.

Democratic officials familiar with the talks said both the cuts to benefit programs such as Medicare and a tax overhaul are too complicated to undertake quickly and would have to wait up to a year to negotiate. The officials, however, said any agreement would have to have strict requirements that would guarantee Congress had to act.

First, however, the Democratic-controlled Senate on Friday dispensed with the House-passed measure that would raise the debt limit by $2.4 trillion on the condition that Congress sends a constitutional balanced budget amendment to the states for ratification and approves trillions in long-term spending cuts.

That left bargaining for a bipartisan compromise as the only alternative. Negotiations were proceeding on multiple fronts as officials searched for the clearest path to avoid a potentially devastating default. Each path faced sizable hurdles.

One short-term plan under discussion by some House Republicans would cut spending by $1 trillion or more immediately and raise the debt ceiling by a similar amount, permitting the government to borrow into early 2012. But Obama has insisted on an increase that lasts into 2013, past next year's elections. That would require raising the debt ceiling by about $2.4 trillion.

White House spokesman Jay Carney said Thursday that Obama remains "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.

Another plan under discussion by Reid and Senate Minority Leader Mitch McConnell, R-Ky., would guarantee that the president would get a debt ceiling increase through 2012. It would extract a political price from Obama, who would have to ask Congress for three separate increments, and it would allow Republicans to avoid casting a difficult vote in favor of the debt ceiling that would anger their constituents. Many House Republicans, however, were dismissive of the proposal because it did not guarantee deficit reductions.

Then there are the efforts by Obama and Boehner to close gaps on a deal to reduce deficits by about $4 trillion.

Democratic officials familiar with the 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. By day's end Obama had asked the top four Democrats in the House and Senate to go to the White House to discuss the status of the talks. The meeting lasted one hour and 45 minutes.

In his opinion piece in USA Today, Obama said he was still insisting on tax revenue being part of the deal. Democratic officials said that Obama was not demanding that specific tax provisions, such as restrictions on tax subsidies or closing loopholes, be agreed upon immediately, but that they could be part of a broader tax overhaul that Congress would have to undertake.

House Minority Leader Nancy Pelosi, D-Calif., left the door open to such an approach to tax changes. "I'd like to see it have a revenue piece so we have tax fairness, whether immediately or something that's part of an extended plan to it," she said Thursday.

The Democratic officials said the negotiations focus on immediate cuts to day-to-day operations of government that are financed at Congress' discretion. The legislative work to cut entitlement programs such as Medicare and Medicaid and to overhaul the tax system would have to be carried out over the next six month to a year, the officials said.

One key sticking point, they said, was how to force Congress to address entitlement and tax changes to achieve the desired deficit reduction. Under discussion were mechanisms that would trigger onerous tax and spending consequences if Congress tried to wiggle out.

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Associated Press writers David Espo, Ben Feller and Alan Fram contributed to this report.

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