President makes surprise appearance at Tuesday briefing, says admin has matched Republicans’ original proposal.

Pledges to “meet as long as possible” to get this resolved.

And: Says admin not invited to Boehner’s meeting with Reid at 4 p.m. Will call another meeting at WH tomorrow if agreement not reached.

Highlights from Obama’s presser:

Says he shouldn’t have to “oversee” a process that deals with last year’s budget when there’s only six months left.

“Happy to listen to ” any additional “reasonable” proposals.

Budget cannot be vehicle to debate every “ideological or political difference” between the two parties.

“We have more than met the Republicans half way.”