The Senate passed legislation instructing the Pentagon to permit military chaplains to conduct worship services. House approval was still needed late Friday.
Keith Colburn, a crab fisherman, told lawmakers during the day that a lucrative, one-month crab harvest set to begin Tuesday in the Bering Sea is in jeopardy because the National Oceanic and Atmospheric Administration is not assigning quotas to boats.
Obama met at the White House for more than an hour with Senate Republicans, the last in a series of four presidential sit-downs with the rank and file of each house and each party.
He has said recently that he is willing to negotiate with Republicans on budget, health care or other issues, but only after the government is reopened and the threat of default eliminated.
The White House seemed to wobble on that point Thursday, until Reid emphatically reinforced that it is his view, too.
Republicans have just as insistently demanded that Obama negotiate with them in exchange for passage of legislation that both sides agree is essential.
This has left Obama and congressional leaders looking for a way to negotiate their way out of an impasse without appearing to negotiate -- with the health of the nation's economy dependent on their political dexterity.
The administration said the government will bump up against its borrowing limit on Thursday, raising the specter of an unprecedented default.
At Obama's meeting with Senate Republicans, Sen. Susan Collins of Maine laid out a proposal to raise the debt limit until the end of January, reopen the government and take a slice out of the health-care law. Under a proposal she and other GOP senators have developed, a medical-device tax that helps finance the health-care law would be repealed, and millions of individuals eligible for subsidies to purchase health insurance under the program would be subject to stronger income verification.
At the same time, federal agencies that have been affected by across-the-board cuts would gain greater flexibility in the use of their remaining funds.
Any other items could be negotiated later.
After returning to the Capitol, Collins said Obama said the proposal was "constructive."
"But I don't want to give the impression that he endorsed it," she said.