The House legislation, approved Wednesday on a bipartisan vote, is the first step toward averting a possible fiscal showdown this month. If another budget crisis can be avoided, it could clear the way for lawmakers and President Barack Obama to restart talks on a longer-term deficit reduction plan.

That was Obama’s focus during a rare dinner with a dozen Republican senators Wednesday night at a hotel near the White House and seemed certain to be Topic A Thursday when Rep. Paul Ryan, chairman of the House Budget Committee and last year’s GOP vice presidential nominee, joined the president for lunch Thursday at the White House.

While no real breakthroughs appeared to emerge from Wednesday’s two-hour meal, the mere fact that it happened was significant given the lack of direct engagement between Obama and rank-and-file Republicans over the past two years.

White House and congressional aides said the president and lawmakers had a good exchange of ideas centered on how they could work together to tackle the nation’s fiscal problems.

Emerging from the dinner, Sen. John McCain jokingly said the meeting was “terrible,” then added that the meal went “just fine” and flashed a thumbs-up.

“It was, I thought, a very sincere discussion,” Sen. Bob Corker, one the dinner attendees, said in an interview Thursday with The Associated Press. “Everybody laid their cards on the table. I thought it was constructive.”

“I do think it helped a lay a foundation that maybe sometime between now and when the debt ceiling hits, which is really around the first of August or that time frame, maybe we’ll get to a much broader and deeper deal as it relates to solving our fiscal problems, ” Corker, R-Tenn., said.

He said that while both sides emphasize different components of a long-term deficit reduction deal, “there is more commonality than people think.”

It would take months for compromise talks on a broad deficit reduction deal to bear fruit, and there is little sign of shifts on the key difference that separates the parties. Obama is seeking higher taxes as part of his deficit-cutting approach, while Ryan, author of the House GOP budget, previewed a longer-term plan Wednesday to erase federal deficits without raising taxes.

“I think this whole thing will come to a crescendo this summer, and 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,” Ryan said. He added that he had spoken with Obama in recent days but declined to provide details.

Obama’s phone call with Ryan and other congressional Republicans, along with Wednesday’s dinner, mark a shift in tactics for a president who has been reluctant to reach out personally to lawmakers. But White House efforts to compel Republicans to negotiate by mounting public pressure campaigns proved futile in the efforts to avert the automatic spending cuts that started taking effect Friday.

Corker said the group had a “frank discussion” about the confrontational tone and public rhetoric that has marked the debate.

“On the one hand, to sit down in a room and be sincere and talk about a problem in a real way, and then to go out the microphones and the cameras and put on the gloves, there was a strong acknowledgment last night that that’s not a way of dealing with our nation’s biggest issues,” Corker said.

Lawmakers and the White House are now looking for ways to ease the impact of the “sequester,” as the automatic cuts are called, at the same time they seek to prevent a shutdown of federal agencies on March 27.

The legislation that cleared the House on Wednesday on a bipartisan vote would do both, ensuring funding through the Sept. 30 end of the budget year while granting the Pentagon and the Veterans Affairs Department greater flexibility in implementing their share of short-term spending cuts.

The bill now goes to the Senate, where Democrats and the White House are deep in negotiations with Republicans on changes that would give the Homeland Security Department and other domestic agencies the same type of flexibility that the Pentagon would receive in administering the spending cuts.

As the president looks toward longer-term talks on deficit reduction, he is pointedly skipping over the Republican leaders of the Senate, Mitch McConnell, and of the House, John Boehner, both of whom insist Obama will get no further tax hikes from Capitol Hill. Instead, aides say, Obama is focusing his outreach on lawmakers with a history of bipartisan deal-making and those who have indicated some willingness to support increased tax revenue as part of a big deficit-cutting package.

Republicans have had mixed reactions to the outreach from the president, who has often preferred assigning those efforts to his staff and Vice President Joe Biden.

“He’s never spent any time reaching out,” said Sen. Tom Coburn, R-Okla., who spoke with the president this week about gun-control legislation. “The question is, is it starting to change because there is bad poll numbers, or is it because he really decided he’s going to lead and solve some of the problems of the country?”

Sen. Lindsey Graham, a frequent critic of the White House on national security issues, said he was encouraged by Obama’s efforts.

“This is how you solve hard problems,” the South Carolina Republican said.

It was during a phone call with Graham this week that the president raised the prospect of a group dinner with Republican lawmakers, an Obama aide said. Graham agreed to put together a guest list.

Along with Graham, Coburn and McCain, the lawmakers in attendance at Wednesday’s dinner were Sens. Kelly Ayotte of New Hampshire, Pat Toomey of Pennsylvania, Corker, Ron Johnson of Wisconsin, Saxby Chambliss of Georgia, John Hoeven of North Dakota, Dan Coats of Indiana, Richard Burr of North Carolina and Mike Johanns of Nebraska.

Obama advisers say they’re hopeful that without the heightened pressure of an imminent fiscal deadline, the president and Republicans can have constructive conversations on a broad deficit-reduction bill that would include concessions from the GOP on tax increases and from Democrats on entitlement programs.

But unless Boehner and McConnell bend on taxes, prospects for a sweeping deficit deal remain dim.

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.

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By Julie Pace, AP White House correspondent. Associated Press writer Jim Kuhnhenn contributed to this report.