In meetings with lawmakers over two days, Obama left open the possibility he would sign legislation repealing a medical device tax enacted as part of the health care law. Yet there was no indication he was willing to do so with a default looming and the government partially closed.
Obama called House Speaker John Boehner at midafternoon, and Michael Steel, a spokesman for the leader of House Republicans, said, "They agreed that we should all keep talking."
Jay Carney, the president's press secretary, said Obama "appreciates the constructive nature of the conversation and the proposal that House Republicans put forward. Yet, the spokesman said, "He has some concerns with it."
In Congress, the man certain to be involved in any final agreement, Senate Majority Leader Harry Reid, gave no indication of his plans.
While the impact of the shutdown varies widely, lawmakers seemed to be taking care of their own needs.
The members-only House gym remained in operation, and enough Senate staff was at work to operate the aging underground tram that ferries senators and others from the Russell Office Building to the Capitol a short distance away.
The shutdown sent ripples nationwide.
The aerospace industry reported that furloughs at the Federal Aviation Administration have resulted in a virtual stop to certification of new aircraft, equipment and training simulators.
The Senate passed legislation instructing the Pentagon to permit military chaplains to conduct worship services. House approval was still needed.
And 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.