Washington (CNN) -- President Barack Obama told congressional Republicans on Wednesday that entitlement reforms were under discussion as part of a deficit reduction deal.
In the meantime, the White House continued to challenge a controversial GOP proposal to overhaul Medicare.
Obama met for 75 minutes with House Republicans a day after the GOP-controlled House overwhelmingly rejected a measure to raise the national debt ceiling without any accompanying deficit- or spending-reduction provisions.
The meeting occurred amid deficit reduction negotiations brokered by Vice President Joe Biden at a time when the nation has reached its debt ceiling and needs congressional authorization to borrow more. While both sides say the negotiations have made progress, they remain far apart on key issues such as tax reform and how to reduce the rising costs of entitlement programs such as Social Security, Medicare and Medicaid.
According to White House spokesman Jay Carney and Republican participants, the meeting was frank and productive but nonconfrontational. However, Republican sources in the meeting said House Budget Committee Chairman Paul Ryan, the initiator of a budget proposal that includes the Medicare overhaul plan, called on Obama to show more leadership on the issue.
The sources said Ryan, R-Wisconsin, urged Obama to stop playing politics with Medicare reforms, saying leaders can either solve problems "or exacerbate them." Ryan also said Obama appeared more focused on winning the 2012 election than solving the nation's problems, according to the sources. After he spoke, his fellow Republicans in the room gave him a standing ovation, the sources said.
Ryan told reporters that he explained the plan to Obama so that the president and Democrats would stop mischaracterizing it to the public.
"I simply explained what our plan is, how it works," Ryan said. "It's been misdescribed by the president and many others, and so we simply described to him precisely what it is we've been proposing, so that he hears from us how our proposal works, so that in the future he won't mischaracterize it."
Republican Rep. David Dreier of California, who attended the meeting, told reporters the discussion between Ryan and Obama "was very friendly and respectful," adding that other GOP members also spoke and "there was strength shown on both sides."
Dreier also said Obama told the House Republicans after Ryan spoke that "entitlements are on the table."
Carney told reporters that the meeting reached no agreements and wasn't designed to, but instead provided Obama and House Republicans a chance to privately discuss the key issues facing them.
"Obviously there are long-term disagreements between Republicans and Democrats, between this president and Republicans," Carney said. "All of those disagreements will not be resolved in the next several weeks as this negotiation moves forward."
One key issue clearly remained unresolved: The GOP proposal to overhaul the government-run Medicare program that provides health care for senior citizens. The proposal, which would increase the health care costs of senior citizens starting in 2022, has prompted public opposition and, last week, helped a Democratic candidate win a special House election in a traditionally Republican district.
Republicans complain that Democrats erroneously say the Ryan plan would mean senior citizens would be forced into the private health insurance market and receive a government payment to cover some of the costs. Republicans contend the plan sets up a Medicare exchange offering specific options for private coverage, with the government helping to pay the bill.
The nonpartisan Congressional Budget Office has said the Ryan proposal would increase the average health care costs for senior citizens by $6,000 a year.
At his daily briefing after the meeting, Carney continued to call the Ryan proposal an effort to end the Medicare system as it now exists. He repeated past phrasing that the Republican plan would "end Medicare as we know it."
He also directly linked the unpopular GOP Medicare proposal with another issue pushed by Obama's Democratic base: Ending tax cuts for the wealthy.
"In order to achieve the (spending) reductions that they seek and pay for the tax cuts that aren't called for, they need to do things to Medicare that aren't necessary," Carney said, calling the debate "a question of priorities."
The House, in a 318-97 vote Tuesday, defeated a measure that would have raised the federal government's debt limit by approximately $2.4 trillion. Republicans voted against it unanimously.
GOP leaders scheduled the vote to show that any attempt to divorce an increase in the debt ceiling from spending reduction efforts -- a move initially favored by the Obama White House -- cannot win congressional approval.
Democrats called Tuesday's vote a dangerous political stunt that risked rattling financial markets. The New York Stock Exchange recorded its biggest loss so far in 2011 on Wednesday, though analysts attributed the showing to other issues including Greece's debt problems and tepid U.S. economic reports.
"Playing chicken with the full faith and credit of the United States is a bad idea," Carney said of political maneuvering over the debt ceiling issue.
The federal government hit its current debt ceiling limit of roughly $14.3 trillion on May 16. Treasury Secretary Tim Geithner has indicated he can keep the country out of default until August 2, but warned of potentially devastating financial consequences after that point.
Geithner will meet Thursday with freshman House Republicans, the core of the conservative wave that won a GOP majority last November, to discuss the debt limit issue, according to a senior GOP leadership aide.
Numerous analysts say that a failure to reach an agreement raising the debt limit could lead to skyrocketing interest rates, a plummeting dollar and a higher cost of living for most Americans.
GOP leaders, who campaigned in 2010 on an agenda of fiscal responsibility, oppose any increase in the debt ceiling without major spending cuts.
House Speaker John Boehner, R-Ohio, made clear after the White House meeting that his majority caucus wants the government to cut more spending than the amount it needs to raise its borrowing limit to pay all obligations.
"This morning I released a letter signed by 150 economists who agreed that if we're going to get serious creating jobs in America, we've got to reduce some of the uncertainty," Boehner told reporters. "Some of that uncertainty's caused by the giant debt that's facing our country. And the fact that if we're going to raise the debt limit, the spending cuts should exceed the increase in the debt limit. Otherwise it'll serve to cost us jobs in our country."
Senate Minority Leader Mitch McConnell, R-Kentucky, has said that any vote in favor of raising the ceiling should be accompanied by significant new cuts in discretionary spending over the next two years, followed by significant changes over the longer term to costly entitlement programs such as Medicare and Medicaid.
The question of how to control the explosive growth in popular entitlements may be the most critical question in the current debate over Washington's fiscal health. Leaders from both parties agree that some kind of change is necessary in Medicare in particular, but differ sharply on scope and shape.
Democrats are pushing for tax increases on wealthier Americans as a way to reduce the need for sharp cuts. They have ripped their GOP counterparts for allegedly taking advantage of the current crisis to try to dismantle a social safety net in place since President Lyndon Johnson's Great Society.
Under Ryan's plan, which aims to cut federal deficits by roughly $4.4 trillion over the next decade, Medicare would be overhauled starting in 2022. The government would no longer directly pay bills for senior citizens in the program. Instead, recipients would choose a plan from a list of private providers, which the federal government would subsidize.
While individuals currently over the age of 55 would not be affected by the changes, numerous political strategists believe the proposal will prove to be deeply unpopular among seniors.
According to a CNN/Opinion Research Corporation survey released Wednesday, 58% of the public opposes the Republican plan on Medicare, while 35% say they support the proposal.
Last year, GOP leaders repeatedly attacked the change to the health care law pushed through by Democrats, arguing that it would weaken Medicare. Republican congressional candidates crushed their Democratic counterparts among voters age 65 and older in the November congressional elections, carrying seniors by a 21-point margin.
While voters have expressed concern over the growing debt, they have also shown strong opposition to major entitlement spending reductions.
Six in 10 voters said in an April 29-May 1 CNN/Opinion Research Corp. poll that they were opposed to raising the debt ceiling. Only 14% of voters, however, supported Medicare spending cuts in a CNN/Opinion Research Corp. survey taken March 11-13.
Sixty percent of voters in the April 29-May 1 survey said congressional Republicans are not acting responsibly in the debt ceiling talks. A slight plurality of voters -- 49% -- said Obama is not acting responsibly.
CNN's Kate Bolduan, Alan Silverleib, Ed Henry, Brianna Keilar and Deirdre Walsh contributed to this report.