House Speaker John Boehner announced late Saturday that he was now looking for a deal about half that size and said that chances for a bigger agreement succumbed to the White House's insistence on substantial new tax revenue.
Administration officials said Obama would press for a bigger bargain one last time at a White House negotiating session Sunday evening.
A deficit reduction agreement is crucial to winning Republican support for an increase in the nation's borrowing limit. The government's borrowing capacity is currently capped at $14.3 trillion and administration officials say the United States will go into default without action by Aug. 2.
Expectations for Sunday's meeting took an abrupt turn Saturday after Boehner informed Obama that a package of about $2 trillion identified but not agreed to by bipartisan negotiators was more realistic.
In a statement, Boehner said: "Despite good-faith efforts to find common ground, the White House will not pursue a bigger debt reduction agreement without tax hikes."
Boehner, R-Ohio, notified Obama of his decision to settle for a smaller number early Saturday evening while the president was at Camp David.
Obama planned to return to Washington on Sunday afternoon. The meeting with Boehner and seven other House and Senate leaders is set for 6 p.m. EDT.
A bipartisan group of lawmakers led by Vice President Joe Biden had already identified, but not signed off on, about $2 trillion in deficit reductions, most accomplished through spending cuts.
"I believe the best approach may be to focus on producing a smaller measure, based on the cuts identified in the Biden-led negotiations, that still meets our call for spending reforms and cuts greater than the amount of any debt limit increase," Boehner said.
After holding a secret meeting with Boehner last weekend, Obama and his top aides said they believed an even bigger figure was attainable if both parties made politically painful, but potentially historic, choices.
Obama set out to build political support for an ambitious package of spending cuts and new tax revenue. But from the moment he proposed it, Republicans said they would reject any tax increases and Democrats objected to spending cuts in their prized health programs for older Americans and the poor and to Social Security.
Entering the weekend, prospects for such a chartbusting deal were low, especially after partisans from both parties attacked it.
White House communications director Dan Pfeiffer said Obama intended to continue to push for as big a deficit reduction number as possible and that tax revenue be part of the mix.
"The president believes that solving our fiscal problems is an economic imperative. But in order to do that, we cannot ask the middle-class and seniors to bear all the burden of higher costs and budget cuts," Pfeiffer said. "We need a balanced approach that asks the very wealthiest and special interests to pay their fair share as well, and we believe the American people agree."
Pfeiffer said: "Both parties have made real progress thus far, and to back off now will not only fail to solve our fiscal challenge, it will confirm the cynicism people have about politics in Washington."
A Republican official familiar with the discussions said taxes and the major health and retirement entitlement programs continued to be sticking points.
Obama wanted Republicans to accept closing some corporate tax loopholes and subsidies to corporations, ending a tax friendly inventory accounting system for businesses, as well as reducing the value of tax deductions for wealthy taxpayers.
A senior administration official said the discussion on taxes broke down over the administration's desire to have the wealthy pick up a bigger share of the tax revenue load than Republicans were willing to accept.
The official, speaking on the condition of anonymity because of the sensitivity of the negotiations, said the $2 trillion to $2.4 trillion in deficit reduction identified by the Biden-led negotiations remains under negotiation and will also require some new tax revenue of up to $400 billion.
Earlier Saturday, in his weekly radio and Internet address, Obama appealed to Democrats and Republicans to "make some political sacrifices" and take advantage of an extraordinary opportunity to tackle the government's budget crisis.
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