ANALYSIS:

Beware of irrational exuberance. Thursday night's meeting between President Obama and House Republican leaders was clearly a breakthrough, but both sides are cautioning this morning that progress is fragile.

One player on the Republican side said he is "mildly optimistic" while a player on the Democratic side said there is "cause for optimism, but we're not a whole lot closer to resolution."

Here's what's happening: In addition to the short-term debt ceiling extension, the talks are focused on getting agreement on a short-term resolution to end the 11-day-old government shutdown and set up a framework for broader budget talks.

Republicans made it clear Thursday night that they need something in exchange for agreeing to end the shutdown. The president told them that he could, in principle, offer only something that he would normally offer through the course of regular budget negotiations; in other words, nothing on Obamacare, no major spending concessions.

What is the Debt Ceiling, Anyway?

Republicans are now working up their proposal. It is unclear whether they will be able to come up with something the White House finds acceptable.

The bottom line: Republicans are working out the terms of their surrender and are attempting to get something for a standoff that has divided the party and cost dearly in the polls. On substance, it is Republicans who are giving in, although the president is now doing something he said he would not do: negotiate while the government is shutdown and there is a threat of default.

He's negotiating, but he's made it clear he is not going to give much.