WASHINGTON (CNN) -- Angry Democrats rejected a proposal from Republicans Saturday for a two-step approach to raising the debt limit as congressional leaders raced against to clock to find a solution to the nation's debt-ceiling crisis, Democratic sources said.
Under the two-step plan put forward by House Speaker John Boehner, the nation's debt ceiling would be raised through 2011 in exchange for spending cuts totaling around $1 trillion, the sources said.
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, they added.
While Democrats and Republicans agreed on the first stage of the plan, they split over how a second ceiling increase would be approved, the sources said.
Specifically, they said 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.
Congressional leaders are anxious to find a solution Sunday in time to head off a negative reaction in Asian markets, according to both Democratic and Republican aides.
Boehner stated this goal in a Saturday afternoon conference call with House Republicans. Boehner favors a plan to cut spending by $3 trillion to $4 trillion in the two-step process, a Republican aide said.
"He (Boehner) said he wanted to get something agreed to prior to Asian market trading (in the new week)," the aide told CNN.
Earlier in the day, President Obama held a one-hour meeting with congressional leaders following the collapse of direct talks Friday between him and Boehner.
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.
One Democratic official involved in the talks said the meeting was not contentious, and the participants did not rehash what went wrong with the Obama-Boehner talks. Rather it was very focused on "just how do we fix it," and "everybody is pretty serious" about finding a way forward that prevents a default, the official said.
However, there was a recognition that the congressional leaders -- all of whom say they want to prevent default -- can only do so much about the opinions and actions of their caucuses, the official said.
"Different people put different ideas on the table" resulting in a mishmash of things that need to be sorted through to see what might be viable, the official said. Congressional staff will be sorting through the different ideas, the official added.
The president repeated his insistence that the debt ceiling be raised through the end of 2012, the source said.
A House GOP aide told CNN that Republicans are "considering calling the president's bluff" on his refusal to sign a bill that doesn't raise the debt ceiling beyond the November 2012 election.
The aide said that party members are "struggling to see how they reach an agreement with significant debt reduction without buying time to work out the details."
Boehner aide Michael Steele had earlier told reporters that "it would be terribly unfortunate if the president was willing to veto a debt-limit increase simply because its timing would not be ideal for his re-election campaign. We want the most significant deficit reduction possible, but linking the full faith and credit of the United States to presidential campaign politics is not a defensible position."
Harry Reid, the Democrat Senate majority leader, reiterated Saturday afternoon that he sided with the president on rejecting any short-term extensions on debt-ceiling discussions.
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