After struggling for weeks and weeks in stages one through four, Republicans are finally entering the final stage of grief over the death of their belief that President Obama would begin offering concessions in exchange for an increase in the debt limit.

The catalyzing event appears to have been an hour-plus-long meeting between Obama and congressional leaders at the White House on Wednesday. Senior administration officials say that if the meeting accomplished only one thing it was to convey to Republican leaders the extent of Obama’s determination not to negotiate with them over the budget until after they fund the government and increase the debt limit. These officials say his will here is stronger than at any time since he decided to press ahead with healthcare reform after Scott Brown ended the Democrats’ Senate supermajority in 2010.

There’s evidence that it sunk in.

First, there’s this hot mic moment in which Senate Minority Leader Mitch McConnell tells Sen. Rand Paul, R-Ky., that the president’s position is ironclad.

Then we learn that House Speaker John Boehner has told at least one House Republican privately what he and McConnell have hinted at publicly for months, which is that they won’t execute their debt limit hostage. Boehner specifically said, according to a New York Times report, and obliquely confirmed by a House GOP aide, that he would increase the debt limit before defaulting even if he lost more than half his conference on a vote.

None of this is to say that Republicans have “folded” exactly, but they’ve pulled the curtain back before the stage has been fully set for the final act, and revealed who’s being fitted with the red dye packet.

If they got the same explanation from the president that I and several other writers got from senior officials at a White House briefing today, they know that for Obama this is more than just about preventing his own personal embarrassment (at having caved) and more than about his individual legacy (which will be harmed even if Republicans bear the brunt of the blame for a default). He sees “right sizing” the executive branch, and leaving it in better shape than when he inherited it, as a core responsibility of his presidency. Reducing the scope of executive powers in the foreign policy realm is one piece of it. But it would be a complete abdication, in his mind, to leave the next president vulnerable to the nullification of his or her election.

This is the crucial context in which to read separate reports that Republicans want to revisit the “grand bargain.” For the most part, this is just a hangover from the denial phase — Republicans talking to each other, trying to convince themselves that they can walk away from the debt limit with some concession. But they’re also hoping to draw Obama into a negotiation he can’t later extract himself from. It’s not going to work, administration officials say. They are happy to entertain budget negotiations after the debt limit increases. And during those negotiations they believe Republicans can legitimately use the leverage sequestration gives them to extract concessions. But only then. No more negotiating over the budget before the debt limit goes up, as long as factions within the Republican Party are prepared to default.

The only thing that might change Obama’s position is if Boehner decided to sprint into his waiting arms, burning his bridges to House conservatives behind him. If Boehner wanted to finish the budget deal he almost reached with Obama late last year, revenue and all, then throw in a debt limit increase, and a budget for the government, Obama wouldn’t freeze him out. But it doesn’t sound like that’s what Boehner has in mind.

Boiling it all down, this means that Republicans only have one viable way to save face. And that is to come up with something non-substantive — a procedural side-car like “No Budget, No Pay” — that’s independent from the debt limit itself, tack it on to a debt limit increase, and put it on the floor.