At the White House, Mr Obama warned time was running out for a bargain, but rejected Republican plans to cut public spending without raising taxes.
Cross-party talks between Mr Obama and congressional leaders have failed to make a breakthrough.
The US must raise its $14.3tn (?8.9tn) debt limit to borrow beyond 2 August.
Failure to reach a deal would rattle a world economy still trying to put the 2008 downturn behind it, analysts say.
'Out of time'Though both Democrats and Republicans have expressed a commitment to averting a financial collapse, Republicans have refused to agree to the tax hikes on corporations and wealthy Americans proposed by Mr Obama.
"I am still pushing for us to achieve a big deal," Mr Obama said in a White House news conference on Friday.
"If we can't do the biggest deal possible, then let's still be ambitious; let's still try to at least get a down payment on deficit reduction."
The president said he was prepared to enact cuts to benefits and welfare schemes, but would need Republicans to consider some revenue increases in return.
"If they [Republicans] show me a serious plan, I'm ready to move even if it requires some tough decisions on my part," the president said, speaking at the White House during the third news conference in two weeks on the issue.
"I am confident that we cannot only impress the financial markets, we can also impress the American people that this town can actually get something done once in a while," he added.But the president warned the country is "obviously running out of time".
"If Washington operates as usual and can't get anything done, let's at least avert Armageddon," Mr Obama said.
The president added that he has told members of Congress "they need over the next 24 to 36 hours to give me some sense of what your plan is to get the debt ceiling raised".
Mr Obama said Republicans have a "unique opportunity to do something big" and stabilise the economy for decades to come, adding that a failure to raise the debt ceiling would mean "effectively a tax increase for everybody".
Republicans, who control the House of Representatives, say they will not raise the debt limit unless Democrats agree to major spending cuts to reduce the deficit, while Democrats have said cuts must be accompanied by some tax increases.
The president said on Friday that "poll after poll" had demonstrated that Republicans are out-of-touch with what voters want,
"The majority of people want a balanced approach to the budget," Mr Obama said.
Meanwhile, Republicans and Democrats emerged from closed meetings on Capitol Hill only to reiterate their stances.
US under reviewOn Thursday, Standard & Poor's became the second of the major credit rating agencies to place US debt under review, citing an increasing risk of a payment default.
Continue reading the main story US government currently runs a $1.5tn budget deficit, requiring it to issue debt in the form of treasury bills, bonds and other securitiesPublic debt was $14.3tn on 31 May, up from $10.6tn when Mr Obama took office in January 2009Most is held by the public, with the rest held in US government accountsCongress has voted to raise the US debt limit 10 times since 2001Sources: US Treasury, Congressional Research Service, Congressional Budget Office
Another ratings agency, Moody's, warned a day earlier that it might cut Washington's triple-A debt rating.If no agreement is reached with the next 24-36 hours, meetings would have to continue into the weekend, aides suggested.
The political impasse boiled over on Thursday to the Senate floor, where Majority Leader Harry Reid, a Democrat, called House Republican Leader Eric Cantor "childish".
Mr Obama needs the Republican-led House of Representatives and Democratic-held Senate to agree a deal to trim the US deficit, and allow Washington to borrow beyond the 2 August deadline.
He has said he is willing to countenance cuts to social safety-net programmes dear to Democrats if certain tax breaks are eliminated.
Republicans have rejected the latter proposal, saying that would stifle investment and job growth.
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