But Senate Majority Leader Harry Reid of Nevada said moments later, "We're locked in tight on Obamacare" and neither the president nor Democrats will accept changes in the nation's 3-year-old health care law as the price for spending legislation needed to end the two-day partial shutdown.
With the nation's ability to borrow money soon to lapse, Republicans and Democrats alike said the shutdown could last for two weeks or more, and soon oblige a divided government to grapple with both economy-threatening issues at the same time.
The White House said in a statement after the meeting that Obama had made it clear "he is not going to negotiate over the need for Congress to act to reopen the government or to raise the debt limit to pay the bills Congress has already incurred."
It added, "The president remains hopeful that common sense will prevail."
The high-level bickering at microphones set up outside the White House reflected the day's proceedings in the Capitol.
The Republican-controlled House approved legislation to reopen the nation's parks and the National Institutes of Health, even though many Democrats criticized them as part of a piecemeal approach that fell far short of what was needed. The bills face dim prospects in the Senate, and the White House threatened to veto both in the unlikely event they make it to Obama's desk.
"What we're trying to do is to get the government open as quickly as possible," said the House majority leader, Rep. Eric Cantor of Virginia. "And all that it would take is us realizing we have a lot in agreement."
Earlier, an attempt by Democrats to force shutdown-ending legislation to the House floor failed on a 227-197 vote, with all Republicans in opposition. That left intact the tea party-driven strategy of demanding changes to the nation's health care overhaul as the price for essential federal financing, despite grumbling from Republican moderates.
The stock market ended lower as Wall Street CEOs, Europe's central banker and traders pressed for a solution. Chief executives from the nation's biggest financial firms met Obama for more than an hour Wednesday, some of them plainly frustrated with the tactics at play in Congress and with the potential showdown coming over the debt limit.
"You can re-litigate these policy issues in a political forum, but we shouldn't use threats of causing the U.S. to fail on its obligations to repay its debt as a cudgel," Lloyd Blankfein, CEO of Goldman Sachs, said after the meeting.
Democrats were scathing in their criticism.
"The American people would get better government out of Monkey Island at the local zoo than we're giving them today," said Rep. John Dingell of Michigan.
The Republican National Committee announced it would pay for personnel needed to reopen the World War II Memorial, a draw for aging veterans from around the country that is among the sites shuttered. In a statement, party chairman Reince Priebus challenged Democrats "to join with us in keeping this memorial open."
Democrats labeled that a stunt. "We've already been working on a plan to open the Memorial — and the entire government — after the GOP caused them to close," said party spokesman Mo Elleithee. "It's called a clean" spending bill.