Washington (CNN) -- President Barack Obama said Friday he has not given up hope for a broad deficit reduction deal, urging Republicans to accept a fiscal stability package that includes higher taxes on the wealthy and reforms to politically popular entitlement programs such as Medicare and Social Security.
Such a measure would be part of plan to avert a potential economic meltdown by raising the nation's current $14.3 trillion federal debt ceiling.
The president also stressed he has not ruled out less ambitious plans focused more narrowly on a debt ceiling increase.
Let's "set politics aside" and "do some tough stuff," Obama told reporters at a White House news conference. But "if Washington operates as usual and can't get anything done, let's at least avert Armageddon."
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 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 it would put the sterling bond rating of the United States on review for possible downgrade.
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 over the last five days, however, 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.
The president told congressional leaders Thursday he expected them to consult with their respective caucuses and find agreement over the next 24 to 36 hours on how to proceed.
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 economic recovery, 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 a balanced budget in the future.
"No one wants the United States to default on our obligations," said House Speaker John Boehner, R-Ohio. But "it's time for Democrats to get serious."
The 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."
Obama repeatedly insisted GOP leaders are out of step with public opinion, arguing most voters support a combination of spending cuts and tax hikes.
Republicans should be "listening not just to lobbyists or special interests," he declared. "This is not just a Democratic understanding."
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 House Majority Leader Eric Cantor, R-Virginia, became particularly tense earlier in the week.
Cantor 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.
On Thursday, Boehner downplayed reports of a split between himself and Cantor. Analysts have speculated that Cantor, viewed in some circles as more conservative than Boehner, may be using the crisis to undermine GOP support for the speaker.
"We're in the foxhole" together, Boehner told reporters Thursday. "I'm glad Eric's there."
One of the issues at 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.
Senate Majority Leader Harry Reid, D-Nevada, confirmed Thursday that he and 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 McConnell 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 the McConnell plan is not the preferred option, but indicated a variation of it could ultimately be accepted in order to avoid a larger crisis.
CNN's Ted Barrett, Kate Bolduan, Jennifer Liberto, Dan Lothian, Jessica Yellin, Kevin Bohn, Deirdre Walsh and CNNMoney contributed to this report.