* Obama, Republicans discussed targets, not specifics
* Entitlement programs on the table
* Pelosi: Democrats won’t support Social Security cuts
* Obama says negotiators will meet again on Sunday (Updates with goal of $3-4 trillion in savings, refiles to insert dropped word)
By Steve Holland and Andy Sullivan
WASHINGTON, July 7 (Reuters) - President Barack Obama and top U.S. lawmakers emerged from talks on Thursday still far apart on breaking a budget deadlock and said negotiators will work through the weekend for a deal to avoid a debt default.
Obama and congressional leaders are aiming for at least $3 trillion and possibly more than $4 trillion in budget savings.
Presented with three possible targets -- roughly $2 trillion, $3 trillion, or more than $4 trillion over a decade -- all the participants agreed to one of the higher figures, Democratic congressional aides said.
The meeting dwelt only with the size of a deal, not policy specifics. A Sunday meeting is to tackle the more difficult question of how those savings can be achieved, the aides said.
But as Obama strives for a deficit reduction deal that would clear the way for Congress to increase the $14.3 trillion cap on government borrowing by the deadline of Aug. 2, he faces a a possible rebellion on his left flank.
The top Democrat in the House of Representatives, Nancy Pelosi, expressed concerns that cuts in popular entitlement programs like Social Security and Medicare might be part of the deficit-reduction deal.
Obama and U.S. lawmakers are aiming for an agreement that will cut government spending, possibly raise taxes, and restore some semblance of order to U.S. fiscal policy. The U.S. deficit is expected to be $1.4 trillion this year.
Full coverage of U.S. budget and debt [ID:nUSBUDGET]
What’s on the table in U.S. debt talks [ID:nN1E75T1ZR]
The U.S. Treasury has warned it will run out of money to pay all of the country’s bills if the debt ceiling is not increased by Aug. 2.
If negotiators fail to reach a budget agreement by then, the government will default, which could push the United States back into recession and cause turmoil in global financial markets.
Briefing reporters after 90 minutes of talks with congressional leaders, Obama said both sides still were far apart and that staff negotiators will work through the weekend to find each side’s bottom line.
He said he will have another round of talks with top Democrats and Republicans on Sunday, hoping to begin “the hard bargaining that’s necessary to get a deal done.”
“Everybody acknowledged that there’s going to be pain involved politically on all sides but our biggest obligation is to make sure that we are doing the right thing,” he said.
Pelosi, who was speaker of the House until Democrats lost control of that in elections last Nov. 2, said Democrats feared the poor and elderly would bear the brunt of budget-cutting.
The two sides have discussed changing the way the government measures inflation to restrain the growth of Social Security benefits and tax breaks, an approach that could save roughly $300 billion over 10 years.
“Do not consider Social Security a piggy bank for giving tax cuts to the wealthiest people in our country. We are not going to balance the budget on the backs of seniors, women and people with disabilities,” Pelosi said.
House of Representatives Speaker John Boehner, told Republicans before meeting Obama that they should know by the end of the week whether a big agreement is possible.
“He said it was maybe 50-50,” a Republican Party aide said. “Whether or not it happens is really dependent on whether they (Democrats) continue to insist on tax hikes.”
Normally a routine vote, the debt ceiling has been embroiled in partisan politics, with Republicans seeking to impose deep spending cuts to reduce the budget deficit, which opinion polls show is a major worry for many Americans.
Obama, seeking to avoid angering his liberal base ahead of his 2012 re-election bid, wants tax increases on the wealthy to lessen the pain of spending cuts.
“I want to emphasize that nothing is agreed to until everything is agreed to and the parties are still far apart on a wide range of issues,” Obama said.
Boehner said comprehensive tax reform is on the table and that changes are needed in benefit programs for the poor and elderly to ensure their long-term viability.
“We believe that comprehensive tax reform, both on the corporate side and the personal side, will make America more competitive, help create jobs in our country, and is something that is under discussion,” Boehner said.
Both sides have long sought a tax overhaul but have never agreed on how to carry it out. Democrats want to eliminate many tax breaks while Republicans generally want lower tax rates.
Boehner’s top deputy in the House, Majority Leader Eric Cantor, signaled the possibility of a compromise on Wednesday by saying Republicans could support ending some of the tax breaks that Democrats have proposed in return for tax cuts elsewhere. (Additional reporting by Laura MacInnis, Thomas Ferraro, Matt Spetalnick, Patricia Zengerle, Richard Cowan and Caren Bohan; Editing by Bill Trott and Christopher Wilson)