Formally speaking, nothing much has changed on the fiscal front since yesterday afternoon: House Republicans have offered a six-week extension of the debt limit while making a CR contingent on budget negotiations; Senate Republicans are looking at a slightly longer debt limit extension and CR in exchange for repeal of the medical device tax, and are talking to Senate Democrats about creating a united front.

But psychologically, a lot has changed, as this report from the New York Times‘ Jackie Calmes and Ashley Parker noted following a White House meeting between the president and House GOP leaders:

Even before the meeting, the White House and its Democratic allies in Congress were all but declaring victory at the evidence that Republicans — suffering the most in polls, and pressured by business allies and donors not to provoke a government default — were seeking a way out of the impasse.

After some fretful weeks, the Democrats believe, Mr. Obama was seeing some payoff for his big gamble this year. Burned by his experience with House Republicans in mid-2011, when brinkmanship over the debt limit hobbled the already weak economy, Mr. Obama began his second term vowing never again to negotiate over raising the ceiling or to give any concessions to Republicans for performing an act that is their constitutional responsibility.

“The good news is that Republicans have accepted the principle that they’re not going to attach conditions to the debt ceiling,” said Representative Chris Van Hollen of Maryland, the senior Democrat on the House Budget Committee. “The bad news is they’ve only extended the debt ceiling for six weeks.”

For House Republicans, the maneuvers represented a near-reversal of their original strategy in September of going to the mat over the debt limit but not shutting down the government. Now, under pressure from falling poll numbers and angry business supporters, they are seeking a compromise on the debt ceiling. Yet for now, they are still refusing to finance and reopen the government without some concessions.

But with Senate Republicans pushing for a reopening of government, that could change. On both the debt limit extension and the CR, much of the difficulty involves creating a way where Republicans can claim they’ve pushed the president into budget negotiations on their terms, without a commitment to such negotiations actually being part of the deal. As Greg Sargent summarized the issue this morning:

A lot of this turns on the fudgability (if that’s a word) of what constitutes Dems “agreeing to talks.” Surely there are ways Dems might agree on some kind of resolution to enter into talks later — a statement of intent — that would not constitute giving Republicans anything in exchange for lifting default threat conditions. In this outcome, Republicans would be essentially raising the debt limit cleanly while calling it a partial victory by claiming they forced Dems to the table.

But Dems need to be very cognizant of the fact that Republicans are fully intent on holding on to the debt ceiling as leverage to extort concessions in the future. If they agree to anything that actually cedes something real in exchange for a debt limit hike — such as real talks under threat conditions — they will have merely postponed the inevitable need to win the larger argument that has paralyzed the system.

So while it looks like one hostage will be set loose over the next few days, moving beyond that may require a greater willingness from Republicans to cut losses than we’ve seen so far–but that is showing signs of intensifying right now–or a lot of lawyerly wording that enables both sides to tout whatever happens as a victory if not a precedent.

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Ed Kilgore is a political columnist for New York and managing editor at the Democratic Strategist website. He was a contributing writer at the Washington Monthly from January 2012 until November 2015, and was the principal contributor to the Political Animal blog.