Washington (CNN) -- After expectations were raised of a possible deal earlier Sunday, weekend talks to resolve the nation's debt-ceiling crisis appeared to reach a new stalemate, as the sides pursued separate plans.

"We've hit an impasse," said a top Democratic official close to the debt talks. "We're trying but there's just no bend on their part."

Asian stocks opened lower Monday, the first reaction in major markets after leaders failed to reach agreement on a deal to raise the U.S. debt limit.

Tokyo's Nikkei 225 was down 0.6% to 10,087 about 90 minutes after the start of trading.

In Sydney, the Australian Stock Exchange's All Ordinaries index was down 0.8%.

Read more about Asian market reaction

President Barack Obama called House Minority Leader Nancy Pelosi and Senate Majority Leader Harry Reid to the White House Sunday evening.

The purpose of the meeting was to update the president on the status of the discussions with Republicans and to share an alternative plan with him, said Democratic sources familiar with the talks.

The mood in the White House is concern, from their vantage point, with the House's inability to resolve the talks, the Democratic sources said.

"Tonight, talks broke down over Republicans' continued insistence on a short-term raise of the debt ceiling, which is something that President Obama, Leader Pelosi and I have been clear we would not support," Reid said in a Sunday night statement after the meeting.

The Senate majority leader said his party is putting together a "$2.7 trillion deficit reduction package that meets Republicans' two major criteria: it will include enough spending cuts to meet or exceed the amount of a debt ceiling raise through the end of 2012, and it will not include revenues."

"We hope Speaker Boehner will abandon his 'my way or the highway' approach and join us in forging a bipartisan compromise along these lines," said Reid.

Sunday night, an Obama campaign official told CNN that the president has canceled his appearance at two fundraising events Monday night in Washington, because of the debt-ceiling situation.

The Obama official said Vice President Joe Biden will attend the events instead.

Earlier Sunday, House Speaker John Boehner told House Republicans in a conference call that an agreement, while not being "cut, cap and balance," should reflect the principles of that package, according to sources familiar with the call. He spoke two days after breaking off talks with Obama on a $3 trillion-plus deficit reduction deal.

"Cut, cap and balance," which 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, was passed by the Republican-controlled House and rejected by the Democratic-controlled Senate last week.

"It will require some of you to make some sacrifices," Boehner told his colleagues on the call, according to a source who participated in the call. "If we stand together as a team, our leverage is maximized, and they have to deal with us. If we're divided, our leverage gets minimized."

Earlier in the day, Boehner told "Fox News Sunday" that his last offer remained on the table, as pressure mounted to avert a looming government default.

Read more of what Boehner has said

But in the conference call Sunday afternoon, he seemed to squash the idea that such a "grand bargain" would be possible.

According to a source familiar with that call, Boehner said he did not mean to anger anyone by what he told Fox about there being an offer on the table. An agreement with the president was not and is not possible, the speaker reportedly said.

Both Boehner, R-Ohio, and Treasury Secretary Tim Geithner said early Sunday a comprehensive deficit deal that would bring Republican support for raising the federal debt ceiling was still an option.

"It may be pretty hard to put Humpty Dumpty back together again, but my last offer is still out there. I have never taken my last offer off the table," Boehner said on "Fox News Sunday."

The speaker's spokesman, Michael Steel, said his boss and Obama spoke on the phone Sunday.

Geithner, meanwhile, told CNN's "State of the Union" that the so-called grand bargain sought by Obama remains in play, but he also opened the door to a two-step process pushed by Republicans that would raise the debt ceiling with some spending cuts now, then bring broader structural and tax reforms next year.

"There's nothing wrong with doing this in stages," Geithner said, but he reiterated that a deal must remove the "threat of default" from the country by settling the debt ceiling issue through 2012 because "you don't want politics messing around with America's faith and credit."

Geithner acknowledged the decision on increasing how much money the government can borrow in order to avoid defaulting on its obligations already has been politicized, saying, "They have taken this a little too far, frankly."

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.

Hard bargaining was likely to continue into the coming week, White House Chief of Staff Bill Daley warned on the CBS program "Face the Nation."

"We may have a few stressful days coming up -- stressful for markets of the world and the American people," Daley said. "In the end, there's no question in my mind, the American government will not default."

Two senators involved in months of bipartisan talks on a separate deficit reduction plan by a group known as the "Gang of Six" expressed concern Sunday over the possibility of a government default.

"I'm not confident" of a deal to raise the debt ceiling, said Sen. Saxby Chambliss, R-Georgia, while Democratic Sen. Mark Warner of Virginia said failure to do so "would be the biggest act of irresponsibility in modern political history."

At the Capitol building, a casually dressed David Krone, the chief of staff for Reid, was seen walking to Boehner's office holding a slip of paper. About 20 minutes later, Krone emerged from the speaker's office still holding his paper and munching on pizza.

Boehner announced Friday he was withdrawing from negotiations with Obama and instead would seek a deal with congressional Democrats, but Geithner said the president was involved in talks throughout Saturday that included congressional leaders from both parties.

On the Fox program, Boehner said the talks broke down last week because Obama and Democrats resisted "real cuts in spending" and demanded tax increases he opposes.

"After over six months of conversations with the president about doing the big deal, about taking a big step in the right direction, it is pretty clear to me that they are just not willing to do it -- that the next election matters more than what's right for the country," Boehner said.

While insisting he would prefer to reach an agreement with Democrats, Boehner added, "If that's not possible, I and my Republican colleagues in the House are prepared to move on our own today."

According to congressional sources from both parties, a possible deal under discussion would involve two stages.

Under the plan, the nation's debt ceiling would be raised through 2011 in exchange for spending cuts totaling around $1 trillion, according to Democratic sources. The ceiling would be raised again, through 2012, after a special commission is set up to find ways to reduce the long-term debt through entitlement and spending cuts and tax reform, the sources said.

While Democrats and Republicans agreed on the first stage of the plan, they split over how a second ceiling increase would be approved, the Democratic sources said.

Specifically, Democrats do not like the idea of tying future debt increases to a commission, which could deadlock and thrust the nation back into the uncertain position it is in today, according to the sources.

Both Geithner and Daley stressed the administration's opposition to requiring two votes by Congress to increase the debt ceiling -- one now and another in the first half of 2012, when the election season will be in full bloom.

When asked if Obama will follow through on his threat to veto such a deal, Geithner told CNN that Democrats in Congress would prevent such a measure from even reaching the president's desk.

"It's not going to make it that far ... so that's not a viable option," Geithner said.

According to Boehner aide Steel, a two-step process is "inevitable" because Democrats have failed to offer a concrete proposal.

The negotiations 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.

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. A House GOP aide said Sunday that timeline is still the goal.

CNN's Brianna Keilar, Tom Cohen, Jessica Yellin, Dan Lothian, Deirdre Walsh, Ted Barrett, Kate Bolduan, Alan Silverleib, Matt Smith, Laurie Ure, Jill Dougherty, Steve Brusk and Ana Sebescen contributed to this report.