Washington (CNN) -- House Speaker John Boehner walked away from debt talks with President Barack Obama's administration Friday, raising the stakes in the country's ongoing effort to stave off national default.

"In the end, we couldn't connect. Not because of different personalities, but because of different visions for our country," Boehner wrote in a letter to his fellow Republicans.

The House speaker said that "a deal was never reached, and was never really close."

"For these reasons, I have decided to end discussions with the White House and begin conversations with the leaders of the Senate in an effort to find a path forward," he wrote.

Speaking to reporters soon after news of Boehner's decision broke, a visibly frustrated Obama said that he has told the Republican and Democratic leaders in Congress to come to the White House on Saturday morning to "explain to me how we are going to avoid default" on the nation's debt. Boehner told reporters at a news conference later he would attend that meeting.

The president said his administration had offered "an extraordinarily fair deal" to cut expenditures and raise revenues, in return for Congress agreeing to hike the nation's debt ceiling. But he said that Boehner "left (him) at the altar" by ending negotiations around 5:30 p.m. Friday.

"I remain confident that we will get an extension of the debt limit and we will not default. I am confident of that," Obama said. "I am less confident at this point that people are willing to step up to the plate and actually deal with the underlying problem of debt and deficits. That requires tough choices."

The negotiations -- necessary to stave off an unprecedented national default that could prove economically devastating -- are testing the ability of leaders on both sides of the aisle to legislate effectively in an era of increasingly shrill and unyielding partisanship.

Republicans, who have railed against the growth of government, remain staunchly opposed to any tax increases. Democrats are trying to protect some of their party's primary legacies -- entitlements such as Social Security and Medicare, programs forged at the height of the New Deal and Great Society.

Speaking after Obama did, Boehner accused the White House of "moving the goalposts" by requesting an additional $400 billion in revenue hikes, a move that he said prompted his decision to call off talks with the president.

The Ohio Republican said members of Congress now "will work together" -- absent representatives from the White House -- to reach a deal that involves spending cuts and raising the nation's debt ceiling. He said he was confident that the government would act to avoid default.

"We can work together here on Capitol Hill to forge an agreement, and I'm hopeful that the president will work with us on this agreement," said Boehner, who compared dealing with the White House to dealing with a bowl of Jell-O.

Senior White House officials, speaking on background, denied moving the goalposts and said they had not expected Boehner would walk away from a deal that would have tied between $3.5 trillion and $4 trillion in new savings to an increase in the debt ceiling.

Republicans and Democrats agreed on a number of points, including $800 billion in revenue increases and certain entitlement reforms, the officials said. They disagreed over an additional $400 billion in revenue hikes and how deep cuts to Medicaid should be, they added.

"Obviously this paper is not going in the shredder," said one senior White House official, suggesting the proposal could be revived.

Another senior administration official said that the White House is not happy about Boehner's timeline in notifying the president, as the house speaker's office was briefing reporters on his decision even before Boehner had returned Obama's call.

House Republican leadership aides told reporters that the White House and Boehner had been discussing a plan that would have tied between $3 trillion and $3.5 trillion in new savings over the next decade to an increase in the debt ceiling, not including revenue.

They stressed that whatever deal moves forward must meet two criteria. Any increase in the debt limit will need to be accompanied by spending cuts or reforms greater than the debt increase, and taxes must not be raised, they said.

Meanwhile, Senate Minority Leader Mitch McConnell, R-Kentucky, said that he found it "disappointing that the talks with the White House (and Republicans) did not reach a favorable conclusion," even as he welcomed the news that the debt-ceiling discussions would be decided in Congress.

"It's time now for the debate to move out of a room in the White House and onto the House and Senate floors, where we can debate the best approach to reducing the nation's unsustainable debt," he said in a statement.

Earlier Friday, the Democratic-controlled Senate rejected the GOP's "cut, cap, and balance" deficit reduction plan, voting 51-46 to set the measure aside and clear a path for further talks on what Democrats insist must be a more centrist measure balancing spending reductions and tax hikes.

"Cut, cap, and balance," which passed the Republican-controlled House earlier in the week, would have tied a debt ceiling increase to sweeping reductions in federal spending, caps on future expenditures, and a balanced budget amendment to the Constitution.

While the measure was never expected to become law, holding votes on it allowed Republicans to demonstrate their preference for steps favored by many in the conservative tea party movement.

Senate Majority Leader Harry Reid, D-Nevada, dismissed the vote Friday morning as a waste of time.

"There is simply no more time to waste debating and voting on measures that have no hopes of becoming law," Reid said. There is "no more time to waste playing partisan games."

Republicans argued that Democrats are obstructing sorely needed spending reforms.

"The House has done its job," Boehner declared. "We have a spending problem. Somebody's got to get serious about cutting spending."

The talks, meanwhile, have become a race against the clock. If Congress fails to raise the $14.3 trillion debt limit by August 2, Americans could face rising interest rates, a declining dollar and increasingly jittery financial markets, among other problems.

"Neither party is blameless for the decisions that led to this debt, but both parties have a responsibility to come together and solve the problem," Obama wrote in an op-ed that appeared in Friday's USA Today. "That's what the American people expect of us."

It is unclear -- even if a deal is reached -- that any sweeping package can be approved by the August 2 deadline.

A Republican source familiar with the negotiations said Boehner told Republican lawmakers Friday that to get the debt ceiling raised by August 2, the House must vote on legislation by next Wednesday -- and that means it must be posted online Monday.

White House Press Secretary Jay Carney signaled to reporters earlier in the week that the president may now be willing to sign a short-term debt limit extension if Democratic and Republican leaders are close to agreement on a broad plan that includes both tax hikes and spending reforms.

Obama previously indicated he would veto any short-term extension.

Meanwhile, lawmakers are also continuing discussions focused on the $3.7 trillion debt reduction blueprint put forward by the "Gang of Six," a group of three Democratic and three Republican senators.

Under the group's proposal, $500 billion in budget savings would be immediately imposed, with marginal income tax rates reduced and the controversial alternative minimum tax ultimately abolished.

The plan would create three tax brackets with rates from 8% to 12%, 14% to 22%, and 23% to 29% -- part of a new structure designed to generate an additional $1 trillion in revenue. It would require cost changes to Medicare's growth rate formula as well as $80 billion in Pentagon cuts.

Obama has praised the plan, calling it "broadly consistent" with his approach to debt reduction because it mixes tax changes, entitlement reforms and spending reductions.

The proposal, however, has been hit with a barrage of criticism from both the right and the left. Conservatives have complained about some of the plan's tax changes, while liberals have warned it would cut entitlement benefits too deeply.

If all else fails, party leaders could still turn to a fallback plan initially put forward by Senate Minority Leader McConnell. The measure would give Obama the power to raise the borrowing limit by a total of $2.5 trillion, but also require three congressional votes on the issue before the 2012 general election.

Specifically, Obama would be required to submit three requests for debt ceiling hikes -- a $700 billion increase and two $900 billion increases. Along with each request, the president would have to submit a list of recommended spending cuts exceeding the debt ceiling increase. The cuts would not need to be enacted in order for the ceiling to rise.

Congress would vote on -- and presumably pass -- "resolutions of disapproval" for each request. Obama would likely veto each resolution. Unless Congress manages to override the president's vetoes -- considered highly unlikely -- the debt ceiling would increase.

The unusual scheme would allow most Republicans and some more conservative Democrats to vote against any debt ceiling hike while still allowing it to clear.

McConnell and Reid are also working on two critical additions to the plan, according to congressional aides in both parties. One would add up to roughly $1.5 trillion in spending cuts agreed to in earlier talks led by Vice President Joe Biden; the other would create a commission meant to find more major spending cuts, tax increases and entitlement reforms.

Changes agreed to by the commission -- composed of an equal number of House and Senate Democrats and Republicans -- would be subject to a strict up-or-down vote by Congress. No amendments would be allowed.

Sources say the panel would be modeled after the Base Closing and Realignment Commission, which managed to close hundreds of military bases that Congress could not otherwise bring itself to shut down.

CNN's Jessica Yellin, Dan Lothian, Deirdre Walsh, Ted Barrett and Alan Silverleib contributed to this report.