WASHINGTON — House Republicans drew stark contrasts with Democrats on tricky budget issues as President Barack Obama came to the Capitol on Wednesday in a stepped-up effort to improve relations with lawmakers whose votes he needs to enact his second-term agenda.

Obama held a rare meeting with House Republicans geared at thawing political gridlock, even though he conceded in an interview airing hours earlier that a political accommodation may be impossible.

“It was good. I enjoyed it. It was useful,” Obama said as he emerged from the roughly 90-minute meeting.

Many Republicans who long have chided Obama for failing to engage their party on the nation’s biggest problems are applauding his newfound outreach, part of a concerted effort by the president to mend ties with Congress in hopes of reaching a grand compromise on fiscal issues.

Neither side is backing down from entrenched positions that have prevented deals in the past, a status quo scenario that Obama acknowledged could preclude any agreement.

“Ultimately, it may be that the differences are just too wide,” he said in an interview broadcast on ABC’s “Good Morning America.”

“If their position is, ‘We can’t do any revenue,’ or ‘We can only do revenue if we gut Medicare or gut Social Security or gut Medicaid, if that’s the position, then we’re probably not going to be able to get a deal,” he said.

The issues separating the two parties are the same as they have been all along — fundamental disagreements over whether to pair tax increases with budget cuts in an effort to rein in the nation’s deficit.

House Budget Committee Chairman Paul Ryan, R-Wis., and fellow Republicans put forward their 2014 budget fully mindful that it would be dead on arrival at the White House and in the Democratic-controlled Senate.

The plan, which the White House immediately panned, doubles down on longstanding Republican proposals to slash funding for programs Obama and Democrats want to protect.

It includes a repeal of Obama’s health care law, a major component of his tenure, and Medicare changes that would shift more of the cost to future patients.