Image copyright AFP

"Nothing is off the table." To be diplomatic that is rather a shift in tone from No 10 who, this time last week, were telling all who would listen that the divorce deal reached with the rest of the EU was the best available and there was no chance of significant changes.

MPs had three choices - Theresa May's deal, no deal, or no Brexit. That's why some Tory MPs were, with gritted teeth, actually on board with the deal. One minister told me "the prime minister and the attorney general have convinced me" there is no chance of significant change on the backstop, so they were going to support the agreement.

With the prime minister, however, heading for a likely thumping defeat if there is no change, guess what - No 10's tone has rather changed too.

The PM is back in touch with some EU leaders, and sources say that they are looking at different options, including potentially reopening the withdrawal agreement, even though they are well aware of the risks that runs. One cabinet minister told me, "she simply has to get something else".

But is this last-minute hope of a shift from the EU real? As my colleague Katya Adler's explained there is nothing straightforward about this. On the face of it, it's pretty extraordinary to imagine that the UK government could be genuinely asking to reopen an agreement that took 18 months to put together, has already been through the grinder on multiple occasions and was only concluded a fortnight ago.

But since the ink dried, it has become clear that the chance of getting the deal through Parliament is very small. One minister said, "it's only a deal if it's ratified". Perhaps for wavering MPs, even the sign of the PM continuing to push for more will make a difference.

It is certainly the case that opposition to the backstop is the main impediment to getting the agreement through Parliament. And both sides acknowledge privately there is a possibility of some kind of clarification, some kind of side letter, to give reassurance.

A cynical historian might suggest that if you stand back for a moment, this kind of very, very last-minute haggling was entirely predictable.

But trust is low. If there were to be any last-minute concessions, or perhaps more likely the promise that they might emerge, MPs currently in the mood for rebelling would want genuine promises, not a last-minute flimsy buy-off.

And whether a solution can be constructed before Tuesday's planned vote is just one question. The bigger one is whether a real way forward can be found at all.