(CNN) -- Evoking compromises of the past, President Barack Obama said Saturday that a commitment to shared sacrifice can break the current impasse on the debt ceiling.
"Let's be honest. Neither party in this town is blameless," he said in his weekly address. "Both have talked this problem to death without doing enough about it. That's what drives people nuts about Washington."
The president spoke as internal discussions continued at the White House. These came a day after Treasury Secretary Timothy Geithner, Chief of Staff Bill Daley, House Speaker John Boehner, R-Ohio, and House Minority Leader Eric Cantor, R-Virginia, met, said a Democratic source familiar with the debt negotiations and a Republican aide.
Obama used his address to reach out to the middle class, reiterating his call for higher taxes on the wealthy and reforms to politically popular entitlement programs such as Medicare and Social Security. He cited budget deals forged by President Ronald Reagan and Democratic House Speaker Tip O'Neill as well as President Bill Clinton and Republican Speaker Newt Gingrich, crediting them with making sacrifices that benefited the common good.
"We are all part of the same country. We are all in this together," Obama said.
Republicans, meanwhile, renewed their call for an amendment to require a balanced budget.
"The only reason this administration doesn't want a constitutional amendment is because they want to keep spending the American people's money," Sen. Orrin Hatch said in the GOP response. "And the only reason congressional Democrats would refuse to pass it, is because they know the people of this country would rise up and quickly ratify it."
While saying he has not given up hope for a broad deficit reduction deal, the president stressed Friday he has not ruled out less ambitious plans focused more narrowly on a debt ceiling increase.
Tense negotiations between top Democrats and Republicans, reflecting core ideological principles on taxes and the size of government, have become a race against the clock. Administration officials have warned that a failure to raise the current $14.3 trillion federal debt ceiling by August 2 could trigger a partial default.
If Washington lacks the money to pay its bills, interest rates could skyrocket and the value of the dollar could decline, among other things.
The seriousness of the situation was reinforced Thursday when a major credit rating agency, Standard and Poor's, said it was placing the United States' sovereign rating on "CreditWatch with negative implications." Moody's Investors Services -- another major rating agency -- said Wednesday that it would put the sterling bond rating of the United States on review for possible downgrade.
Hatch, R-Utah, argued that Obama refuses to reform entitlement programs and is pushing "job-killing tax hikes."
"The solution to a spending crisis is not tax increases," he said.
The six-term senator had a different memory of the deal brokered between President George H.W. Bush and House Republicans.
"We've been down this road before," he said. "In 1990 Congress and the president struck a deficit reduction deal that combined spending cuts with tax increases. Unfortunately, while the tax hikes remained, the spending restraint did not, and our debt has marched higher."
Obama warned this week he could not guarantee that older Americans will receive their Social Security checks next month if a deal is not reached. GOP leaders accused the president of resorting to scare tactics.
Talks this week have failed to produce a concrete deal. Obama has suggested that a sixth meeting could be held this weekend if sufficient progress isn't made, according to a Republican aide familiar with the latest negotiations.
As of Saturday afternoon, congressional leaders had been asked by the White House to be "on call," said two congressional aides -- one Democratic and the other Republican.
"We are keeping the lines of communication open with all parties," Michael Steel, a spokesman for Boehner, said Saturday. "Meetings have been occurring, ideas are being exchanged, and scenarios are being discussed. But there is nothing to report in terms of progress."
House Republicans have shown no sign of accepting higher taxes on the rich as part of a so-called "balanced" approach to debt reduction. GOP leaders, who consider tax hikes detrimental to the economy, blasted the president Friday morning for failing to produce what they consider to be a legitimate spending cut plan.
The Republicans also said they intend to move forward with a vote next week with the "cut, cap, and balance" plan -- a blueprint to significantly cut spending, cap future expenditures and amend the Constitution to require the balanced budget.
"No one wants the United States to default on our obligations," Boehner has said. But "it's time for Democrats to get serious."
That plan, favored by tea party conservatives, has virtually no chance of passing Congress. Obama indicated Friday he believes the plan is little more than a political stunt to appease conservatives, and argued it would require "substantial" cuts to Medicare and Social Security.
He also dismissed the push for a constitutional amendment, arguing that political leaders should just "do our jobs."
The president said he is still willing to tackle entitlement reform -- something opposed by elements of the Democratic base -- but stressed it could not be done at the expense of current benefit recipients and not in a way that would fundamentally alter the nature of the programs.
Obama made it clear at Thursday's negotiations that he still favors a package that generates savings of approximately $4 trillion over roughly the next decade, a Democrat familiar with the talks told CNN.
Fallback plans that take major entitlement reform and tax hikes off the table may include between $1.5 trillion and $1.7 trillion in savings previously agreed to in talks led by Vice President Joe Biden.
Administration officials have also discussed extending and possibly expanding the payroll tax cut -- a nod to sagging employment figures -- as well as extending unemployment insurance, according to a Democratic official familiar with the talks.
Obama said Friday that reports the talks have become "ugly" in the last week are overblown. Multiple sources, however, have indicated that discussions between the president and Cantor became particularly tense earlier in the week.
The Virginia Republican has floated the idea of a short-term debt ceiling hike, while Obama is seeking an increase lasting at least through the end of the 2012 campaign.
One of the issues at the heart of the current debate is Obama's call for more tax revenue by allowing tax cuts from the Bush presidency to expire at the end of 2012 for families making more than $250,000. His plan would keep the lower tax rates for Americans who earn less.
Obama noted earlier this week he is not looking to raise any taxes until 2013 or later. In exchange, the president said, he wants to ensure that the current progressive nature of the tax code is maintained, with higher-income Americans assessed higher tax rates.
But resistance to higher taxes is now a bedrock principle for most Republicans, enforced by conservative crusaders such as political activist Grover Norquist. Norquist's group, Americans for Tax Reform, has sponsored a high-profile pledge to oppose any tax increase.
The pledge has been signed by more than 230 House members and 40 senators, almost all of them Republicans.
Harry Reid, the Senate majority leader, confirmed Thursday that he and Senate Minority Leader Mitch McConnell are working on a possible debt ceiling measure that could come up in the event the broader negotiations fail to reach agreement. It is based in part on a plan the Kentucky Republican unveiled this week that would set up three short-term increases in the debt ceiling while at the same time registering the disapproval of Congress for such a move.
McConnell's proposal would give Obama power to raise the debt ceiling by a total of $2.5 trillion, but also would require three congressional votes on the issue before the 2012 general election.
Both Obama and Boehner said Friday that the McConnell plan is not the preferred option. But they indicated a variation of it could ultimately be accepted in order to avoid a larger crisis.
CNN's Jessica Yellin, Deirdre Walsh, Alan Silverleib and Tom Cohen contributed to this report.