WASHINGTON (AP) -- Deadline approaching, President Barack Obama said he and congressional leaders worked through a “very constructive” debt-crisis session Thursday with congressional leaders but the parties were still far apart on deficit reduction proposals. He said he would reconvene the negotiators on Sunday.

Thursday’s meeting came amid signals that the White House was willing to reduce costs for major benefit programs including Social Security and Medicare, while Republicans indicated they might consider new steps to generate government revenue.

“People were frank,” Obama said, just moments after adjourning the one-and-a-half hour meeting with the eight lawmakers who make up the bipartisan leadership of Congress.

Obama acknowledged that the ultimate agreement will not satisfy partisans on both sides, but he said the deal would require both Republican and Democratic votes to pass Congress.

“Everyone acknowledged that pain will be involved politically on all sides,” he said.

Obama met with the leaders of both parties around a table in the White House Cabinet Room as they struggled to reach a deal on raising the government’s debt limit with less than four weeks remaining before a possible first-ever default on U.S. financial obligations. The Obama administration says the government needs to raise the current $14.3 trillion debt limit by Aug. 2.

Obama said every congressional leader in the White House meeting Thursday agreed an agreement needed to be reached before Aug. 2.

Returning to the Capitol after the meeting, House Speaker John Boehner said: “We had a conversation. It was productive.”

While discussions on trimming the costs of entitlement programs had centered on Medicare, the health care program for older Americans, the White House is revisiting a proposal raised earlier in the negotiations to change the inflation measurement used to calculate Social Security cost-of-living adjustments, thus reducing annual increases, officials said Thursday.

The White House has also said the president is aiming for deficit reduction closer to $4 trillion over 10 years - an ambitious number that would nearly double the roughly $2 trillion that had been at the center of negotiations.

Democratic and Republican officials familiar with the discussions said Thursday that Social Security was in the mix for potential cost savings. Reintroducing the retirement program to the talks is likely to cause anxiety among congressional Democrats who have insisted that Social Security does not contribute to the nation’s deficit problems. White House spokesman Jay Carney said the same after Obama spoke.

The officials spoke on the condition of anonymity because of the sensitivity of the talks. They stressed that no aspect of the deal had been accepted by either side.

Obama ignored a question about Social Security during a photo session at the beginning of the meeting. Carney also declined to discuss options before the negotiators.

Liberal groups objected to including Social Security in the talks, and the idea drew mixed reactions from congressional Democrats.

Rep. Rob Andrews, D-N.J., said he would like to know who would be affected by a lower cost-of-living increase and when.

“That’s something we ought to consider,” he added. “I’d want to see the specifics, but I think it’s a plausible and reasonable idea.”

But Rep. Jan Schakowsky, D-Ill., said she would “absolutely” vote against any package that included savings in Social Security spending. “Social Security has zero to do with the deficit. Nothing. It is a completely separate discussion,” she said.

She said she opposed “the very idea of having these essential programs on the table, being forced to put them on the table by Republicans who want to protect the wealth of the wealthiest Americans.”

One official familiar with the negotiations said that an option under discussion would allow Republicans to make a commitment to overhaul and simplify the tax system, an effort that would lower individual and corporate tax rates while closing loopholes, ending some deductions and limiting other tax subsidies. Those changes could generate tax revenue and were a central element of a deficit reduction plan proposed by a bipartisan commission early this year.

Some Republicans argue that a simplified tax system would increase economic activity and that in itself would result in increased tax revenue.

Amid media reports Thursday of Social Security’s inclusion in the debt-cutting talks, Obama spokesman Carney pushed back.

“There is no news here - the president has always said that while Social Security is not a major driver of the deficit, we do need to strengthen the program,” Carney said, providing that any such effort “doesn’t slash benefits.” His statement did not directly address the possibility of reducing annual Social Security increases by changing the inflation adjustments.

Later, while briefing reporters, Carney added: “We have not put restrictions on what is brought into the room or put on the table.”

Two Democratic officials allied with Obama said the president believes it would be easier to win bipartisan support in the House and Senate for a deal that embraces larger deficit cuts closer to the $4 trillion over 12 years that Obama proposed in April.

The officials, speaking on the condition of anonymity to discuss the private negotiations more freely, said the precise number was still in flux, but they said Obama would be making the case for more rather than less deficit reduction in his discussions with congressional leaders Thursday. The negotiations were the first official sit-down since last month, when House Majority Leader Eric Cantor, R-Va., left talks that had been led by Vice President Joe Biden, citing an insistence by Democrats on raising taxes.