President Barack Obama and John Boehner, the top Republican in Congress, are pressuring each other to open the way for votes to end the government shutdown and raise the federal debt limit.
But neither side was showing signs of capitulating even with a potential economy-shaking federal default edging ever closer.
Republicans were demanding talks on deficit reduction and Mr Obama's 2010 health care overhaul law as the price for boosting the government's borrowing authority and returning civil servants to work. Mr Obama wants Congress to first end the shutdown and extend the debt limit.
The government has been partially shut since October 1 because of Congress' failure to pass a normally routine temporary spending bill. Mr Obama also wants Congress to extend the government's borrowing authority - another once-routine matter - warning that if it fails to do so by October 17, the United States will not be able to pay its bills.
Amid the tough talk, though, were indications that both sides might be open to a short-term extension of the borrowing limit and a temporary end to the shutdown, giving them more time to resolve their disputes.
Mr Obama used a White House news conference to say he "absolutely" would negotiate with Republicans on "every item in the budget" if Congress first sent him short-term measures halting the shutdown and the extending the debt limit.
An Associated Press-GfK survey indicated the Republicans may end up taking the biggest hit in public opinion from the fiscal paralysis, just as that party did when much of the government closed 17 years ago during Bill Clinton's administration.
Overall, 62% mainly blamed Republicans for the shutdown. About half said Mr Obama or the Democrats in Congress bear much responsibility.
The back-and-forth came as the financial world flashed unmistakable signs that it feared Washington's twin battles could hurt the economy. The International Monetary Fund trimmed its global and US growth forecasts for 2014, warning that failure to renew the debt limit would raise interest rates and potentially shove the American economy back into recession.
The Obama administration has said that unless Congress acts, it expects to have an estimated 30 billion dollars in cash left by October 17 which is pocket change for a government that can spend tens of billions more than that on busy days and 3.6 trillion dollars a year.
Hitting that date without congressional action would risk an unprecedented federal default that would wound the economy and deal lasting harm to the government's ability to borrow money, many economists warn.
Some Republicans have downplayed the significance of the deadline, saying that even then, the United States would be able to pay China and other holders of U.S. debt.
But Mr Obama said they were badly misguided, warning that default would harm the economy, cause pensions to shrivel and houses to lose value.