WASHINGTON — House Republicans are sending mixed signals in agreeing to meet with President Barack Obama for talks over the budget impasse, while Obama is conceding that a political accommodation may be impossible.

On the one hand, 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.

On the other hand, 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.