With the shutdown in its ninth day Wednesday and a potential economy-shaking federal default edging ever closer, neither side was revealing signs of bending.
But amid the tough talk, Obama invited all 232 House GOP lawmakers to come to the executive mansion on Thursday. Republicans said only 18 would attend, including their leaders and some committee chairmen.
"It is our hope that this will be a constructive meeting and that the president finally recognizes Americans expect their leaders to be able to sit down and resolve their differences," said Brendan Buck, a spokesman for House Speaker John Boehner, R-Ohio.
On Wednesday, Boehner and House Majority Leader Eric Cantor, R-Va., met for 40 minutes at the Capitol with House Minority Leader Nancy Pelosi, D-Calif., and No. 2 Democratic leader Steny Hoyer of Maryland. Each side said the other had requested the meeting, and neither reported any progress in resolving budget differences.
Even so, there were hints of a brief truce, indications that both sides might be open to a short-term extension of the $16.7 trillion borrowing limit and a temporary end to the shutdown, giving them more time to resolve their disputes.
Obama was huddling with House Democrats Wednesday afternoon as both parties looked for a way forward.
So far, the underlying standoff remains the same. Republicans demand talks on deficit reduction and Obama's 2010 health care law as the price for boosting the government's borrowing authority and returning civil servants to work. The president insists that Congress first end the shutdown and extend the debt limit before he will negotiate.
"Speaker Boehner could end this government shutdown today, an hour from now" by letting the House vote to do so, Senate Majority Leader Harry Reid, D-Nev., said Wednesday.
Don Stewart, spokesman for Senate Minority Leader Mitch McConnell, R-Ky., said GOP senators hoped that when they meet Obama - at a time not yet set - he would be willing to bargain.
"But if this is a meeting where he simply reiterates that he won't negotiate, this meeting will not be productive," Stewart said.
On Tuesday, Boehner told reporters he was not drawing "lines in the sand." He sidestepped a question about whether he'd raise the debt limit and fund government for short periods by saying, "I'm not going to get into a whole lot of speculation."
Hours later, 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.
"There's a crack there," Boehner said of the impasse late Tuesday, though he cautioned against optimism.
The financial world is flashing its own signs that it fears Washington's twin battles could hurt the global economy.
On Wednesday, the International Monetary Fund's financial counselor, Jose Vinals, said a failure by Congress to raise the federal debt ceiling and a subsequent U.S. default would cause "a worldwide shock."
Also, the National Retail Federation became the latest business group to urge lawmakers to quickly end their standoff. In a letter to congressional leaders, federation President Matthew Shay wrote Congress must "reverse the economic crisis it has created through the shutdown while it is still a short-term crisis and not the beginning of another recession."
The Obama administration has said that unless Congress acts, it expects to have an estimated $30 billion in cash left by Oct. 17. That is pocket change for a government that can spend tens of billions more than that on busy days and $3.6 trillion 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 expressed doubt that the damage would be as severe.
In the House, Republicans were continuing their tactic of pushing through narrowly targeted bills - over Democratic objections - that would restart popular parts of the government.
On Wednesday, the chamber voted 425-0 to finance death benefits for families of fallen U.S. troops. Blaming the shutdown, the Pentagon has halted the $100,000 payments, usually made within three days of a death.
The stoppage of those payments drew the attention of Senate chaplain Barry Black, who in his prayer opening Wednesday's Senate session said, "When our federal shutdown delays payments of death benefits to families of children dying in faraway battlefields, it's time for our lawmakers to say, 'Enough is enough.' "
But an official of a conservative group that has pressed Republicans to try repealing Obama's health care law was unyielding, saying that fight should continue.
"We should not fund the government until we address the president's unfair, unaffordable and unworkable law," Michael Needham, chief executive officer of Heritage Action for America, said at a Christian Science Monitor breakfast.
Democratic senators took to the Capitol's steps to call on Republicans to reopen the government. But they struggled to be heard over chants from a nearby rally of Washington, D.C., residents asking Senate leaders to clear House-passed legislation letting the city use its own tax dollars to provide services.
D.C. Mayor Vincent Gray spoke briefly to Reid, who with other Democrats is blocking approval of House-passed bills reopening specific programs and is instead insisting the entire government be reopened.
"I'm on your side. Don't screw it up, OK? Don't screw it up," Reid was heard to tell Gray.
Associated Press writers David Espo, Julie Pace, Andrew Taylor and Donna Cassata contributed to this report.