Washington (CNN) -- President Barack Obama and congressional leaders from both parties launched a new round of negotiations on a deficit reduction deal Thursday and quickly scheduled a second meeting for Sunday, signaling a shared desire to ensure the federal debt ceiling gets raised to avoid possible default next month.

The 90-minute White House meeting was described as "very constructive" by Obama and "productive" by House Speaker John Boehner, who has emerged as the chief Republican negotiator. However, no details of the talks were officially announced, and White House spokesman Jay Carney said there was no breakthrough.

Others taking part in the talks included Vice President Joe Biden, Senate Majority Leader Harry Reid, Senate Minority Leader Mitch McConnell and House Minority Leader Nancy Pelosi.

Obama then made a brief statement to reporters in which he announced that the same group of leaders will reconvene at the White House on Sunday. At that point, "the expectation (is) the parties will at least know where each other's bottom lines are, and will hopefully be in a position to then start engaging in the hard bargaining that's necessary to get a deal done," Obama said.

The "parties are still far apart," Obama stressed, adding that everyone recognizes the need to reach an agreement and has conceded there will be "pain involved politically on all sides."

Boehner told House Republicans earlier in the day that the odds of reaching a deal are "maybe 50-50," according to a GOP aide. Republican Sen. Roy Blunt of Missouri, who did not take part in the meeting, said later that "there is a substantial belief that whatever's going to happen is likely to happen in the next few days."

"We'll see how genuine everyone is in trying to get there," Blunt told reporters.

Treasury Department officials have warned that the current $14.3 trillion debt ceiling has to be raised by August 2 to avoid a potential default, which they warn would cause great harm to the nation's economic recovery.

Obama said in Thursday's meeting that he will not sign any agreement that fails to raise the debt ceiling beyond the 2012 election, according to two congressional sources with knowledge of the talks.

The president also has signaled a willingness to include reforms to popular entitlement programs such as Social Security and Medicare as part of a broad agreement for between $3 trillion and $4 trillion in deficit cuts over the next decade, said Democratic officials familiar with the negotiations.

Defense spending and tax reform are also on the table, the officials told CNN.

"Nobody's plan is going to be the plan that emerges," Carney said. "Comprehensiveness and balance are our targets."

Before the meeting, GOP leaders took a hard line against tax hikes as part of any debt ceiling deal.

"Everything is on the table except raising taxes on the American people," Boehner said. "We are not going to raise taxes on the very people that we expect to reinvest in our economy and to help create jobs."

Congressional Democrats, meanwhile, wrestled with rising anger among liberal House members in the wake of news that the president might agree to entitlement cuts.

A group of progressive House Democrats said Thursday morning they are collecting signatures for a letter to Obama opposing any reductions in Social Security, Medicare, or Medicaid. The members warned that they would oppose any deal that cuts entitlement programs or fails to raise taxes on the wealthy.

"We feel that the discussions have been skewed up to this point," said Rep. Raul Grijalva, D-Arizona. We need to protect "programs that are essential to working folks and the middle class."

"The debt must be addressed, but it should be done in a way that is fair to all," said Rep. Judy Chu, D-California.

The politically influential AARP, formerly the American Association of Retired Persons, also weighed in, warning it would oppose any deal cutting Social Security.

"AARP urges all lawmakers to reject any proposals that would cut the benefits seniors have earned through a lifetime of hard work," said Barry Rand, the organization's CEO.

Pelosi, D-California, told reporters later that she wants Obama to "have the room" to reach a deal, and she offered her "full cooperation to do that." However, she said, House Democrats "do not support cuts in benefits for Social Security or Medicare," and negotiations on specific reforms to those programs should be separate from a broader deficit reduction deal.

In addition, Pelosi linked entitlement reforms to Democratic calls for eliminating Bush-era tax cuts for wealthy Americans by restoring higher tax rates for families earning more than $250,000 a year.

"Do not consider Social Security a piggy bank for giving tax cuts to the wealthiest people in our country," Pelosi said.

David Krone, Reid's chief of staff, said that the Democratic leadership's message "is that we want as robust a deficit reduction deal as possible, but it has to be balanced between spending and revenues, in terms of timing, specificity and dollars."

Specifically, CNN has learned negotiators are considering the possibility of raising the Social Security retirement age and trimming benefit levels for older Americans with incomes over $60,000.

Cuts in the range of $500 billion are being considered for Medicare, Medicaid and Social Security, a congressional aide close to the negotiations said. Democrats like Reid, D-Nevada, have long rejected such cuts.

The House returned to work Wednesday from its Fourth of July break, a day after the Senate cut short its recess to come back to Washington. The aide, however, insisted the only real talks going on are between Obama and Boehner, who are holding discussions "in good faith." The two men met over the weekend, a Republican official told CNN.

If Obama and Boehner, R-Ohio, reach an agreement on such an ambitious package, they realize it will likely be met with stiff opposition from lawmakers in both parties, the aide said. Tea party-backed conservatives will oppose revenue hikes, and liberal Democrats will oppose entitlement cuts.

That said, the aide indicated, Obama and Boehner believe they can each gain politically from making attempt to cut a grand deal -- even if it is rejected -- because the public would see they tried to take bold steps to solve the problem. If it is rejected, the two can fall back on a $2.4 trillion deal put forth before the talks collapsed.

McConnell, R-Kentucky, will likely reject such a deal, in part because Republicans believe they have a better chance of winning back the Senate if a long-term deal fails, the aide said.

Democrats are confident Republicans will ultimately agree to some revenue changes -- such as a hike in some fees and the closing of some unpopular tax loopholes. But it will be much more challenging to get them to agree to significant and costly reforms like the capping of tax deductions for people earning more than $250,000 per year, the aide said.

If Republicans ultimately reject any revenue increases and Congress can't raise the debt limit, Democrats believe Republicans will be blamed for causing a default, according to the aide.

Publicly, both sides continue to rail against proposals by the other.

Obama said Wednesday he wants a deal with Congress in the next two weeks, but didn't rule out using a constitutional argument to increase how much money the government can borrow.

"I don't think we should even get to the constitutional issue," Obama said during a Twitter town hall at the White House in response to a tweeted question on whether he would rely on a clause in the 14th Amendment to unilaterally raise the debt ceiling.

The debt ceiling should not be "used as a gun against the heads of the American people to extract tax breaks for corporate jet owners," Obama said, calling for "a balanced approach where everything's on the table."

McConnell objected to the president's characterization of his side's positions as absolutist or maximalist.

"We have a better term for it -- common sense," McConnell said in reference to GOP opposition to tax increases and more government spending in some areas.

CNN's Jessica Yellin, Ted Barrett, Brianna Keilar, Alan Silverleib, Tom Cohen, Kate Bolduan, and Deirdre Walsh contributed to this report