There's also no guarantee Obama and lawmakers won't find themselves facing a fiscal crisis in the coming months. The Senate still has to pass a bill funding the government after March 27 - the House passed its version of the measure Wednesday - and lawmakers will have to decide whether to raise the nation's debt limit in May.
Longer term, Rep. Paul Ryan previewed a 10-year plan on Wednesday that he said would eliminate federal deficits without raising taxes. That would tend to continue the budget standoff between the Republicans and Obama, who wants increased tax revenue to be part of any deal. But Ryan, the GOP vice presidential candidate in 2012, held out hope for communication across party lines.
The Wisconsin congressman, who also has spoken with Obama in recent days, said that "we're going to have to talk to each other to get an agreement about how to delay a debt crisis, how to save this country from a fiscal train wreck that's coming."
The president will have an opportunity to make his case to GOP leaders next week when he heads to Capitol Hill for separate meetings with the House and Senate Republican conferences. McConnell announced that Obama would attend the GOP Senate policy lunch, while Boehner's office said it was still working on a date.
Obama will also meet on Capitol Hill next week with House and Senate Democrats. The White House says all of the meetings were scheduled at the president's request.
White House aides said that while Wednesday's dinner would focus more narrowly on budget issues, the agenda for the lunches will be broader and will include discussions on immigration and gun control.
Even as Obama steps up his engagement with lawmakers, aides say he'll keep trying to build public support for his agenda and continues to believe pressure from the American people can force Republicans into action. Organizing for Action, a group run by former Obama campaign officials, sent an email Wednesday blaming "Republican obstructionism" for the sequester and urging supporters to sign a petition calling on Congress to back the president's approach for offsetting the cuts.
Associated Press writers Donna Cassata, Jim Kuhnhenn, Josh Lederman and Erica Werner contributed to this report.
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