The Prime Minister's whole game now is to persuade the leaders of the EU27 nations that if they were to ditch or to put a time limit on the widely hated backstop, her and their Brexit plan would be ratified at last by MPs.
Can she persuade them?
Well with backbench MPs poised via a vote on the Cooper/Boles amendment to force Theresa May to plead with the EU to delay the moment the UK leaves the EU and take a no-deal Brexit off the table, Brexiters are panicking that a referendum and staying in the EU will soon become the default position.
So both the DUP and the Brexiters of the European Research Group have come over all emollient in respect of the PM's deal - saying very publicly that so long as the backstop dies, her version of Brexit could possibly live (and there'll be more of this from ERG chairman Jacob Rees-Mogg at lunchtime).
Many of them would hold their noses and support her deal, shorn of the backstop, they say.
Which puts the EU in a tight spot. Because the PM has to shift the votes of a staggering 116 MPs to win second time round, and the best she would be able to say to the EU27's prime ministers - in the words of one of her ministerial colleagues - is that she could "possibly" win.
And such a win would not be obtained by a further backstop fudge. The position, in the worlds of one rebel MP, is that "if they bury the backstop and drive a stake through its heart, the deal might squeak through by a handful of votes but it would be close."
What will determine whether the EU would make such a huge leap, to rescue Theresa May and the deal?
Here is the thinking that is going on in EU capitals, relayed to me by a senior official from one of them:
"Given that the majority of two thirds [of the Commons] by which the Withdrawal Agreement [or Brexit deal] was defeated is composed of Unionists, hard Brexiteers as well as Remainers, it would take very clear evidence that it is 'only' the backstop that prevents passage of the WA.
"Theresa May (or whoever) would have to be able to show there is a large and stable majority for the WA on such a basis, and a majority good enough to deliver not just the meaningful vote, but also the ratification and adoption of all necessary UK internal legislation [that will translate the deal into an orderly Brexit on by 29 March].
"I don't think that at the moment anyone is convinced about that. And all MPs seem to want to talk about is the future relationship - not the backstop".
Let us not forget that as recently as December the EU27 rejected a request from the UK to have even an "aspirational" termination date grafted into the backstop. And the Polish foreign minister's suggestion of a five-year time limit earlier this week was swiftly slapped down.
So although the PM will take considerable comfort from the moves by Mogg and the DUP to tone down their rhetoric against the broader tapestry of her deal (which of course still repels them), she will need much more from them if the EU27 leaders are to make the kind of compromise which all history suggests they will never make.
The Brexiters and DUP will need to prove beyond reasonable doubt both that they would vote for a Withdrawal Agreement stripped of the Brexit, and that they command sufficient numbers of votes to carry it over the line.
It is that requisite very public endorsement by Mogg of May and the iteration of Brexit he despises that, to put it mildly, stretches credibility. Have stranger things ever happened?