No 10 hopes MPs see today's vote as the last chance to avoid a no-deal Brexit. But is it?

Not if Oliver Letwin's amendment to the meaningful vote motion passes.

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Deal or no deal: that's the binary choice Boris Johnson would like MPs to believe they face when they vote on his revised withdrawal agreement at the end of the first Saturday sitting of the Commons in 37 years today. But will they buy it?

Until yesterday, it had appeared that the Prime Minister would get his way. Jean-Claude Juncker, Leo Varadkar and most notably Emmanuel Macron have all said – with varying degrees of conviction – that there will be no further extension to the Article 50 period if MPs vote down the deal today.

Those interventions are transparently designed to be helpful to No 10 and ought be taken with a pinch of salt in any case: the EU27 have never been inclined to pull the trigger on a no-deal scenario and they aren't going to start now. Yet they have nonetheless allowed Johnson and his whips to plausibly argue, particularly to the deal-inclined Labour MPs he needs to convince in the absence of the DUP, that it is finally drinking-up time in the last chance saloon.

But is it? Not if Oliver Letwin's amendment to the meaningful vote motion passes. The Tory grandee wants MPs to withhold their approval for the deal until the legislation giving it legal effect – the Withdrawal Agreement Bill – is safely passed onto the statute book. Though Letwin is insisting that the amendment is not intended as a rejection of the deal, it will have precisely the same effect as one – namely that it would require the Prime Minister to seek a further delay under the terms of the Benn Act tonight.

Betting against Labour MPs finally biting the bullet and voting for a deal has never lost anyone money – and nor has lumping on MPs of all stripes opting to give themselves more time to talk. On the former front, it is clear that No 10 are jittery. Only seven have publicly declared they will go through the aye lobby with the government, at least four or five short of the number Johnson needs to be absolutely sure he is safe. To that end, he has promised to include their biggest asks, protections for workers' rights and the environment, in the deal legislation.

But that promise alone is an invitation to vote for Letwin's amendment: the alacrity with which Johnson chose to abandon the DUP when it suited him is hardly a great advertisement for the reliability of his word. Delaying approval of the deal until the Bill becomes law will allow them to bank those commitments. So what happens if it goes through? As Stephen argues here, that's really up to the government: it can declare it a victory and attempt to pass the deal legislation as quickly as it can, or it can bank the extension and go to the country on the back of parliament blocking Brexit.

Or it might turn out that the government has the votes not only to pass its deal, but to defeat Letwin's amendment, too. What is clear is that Johnson is closer to doing the former than Theresa May ever was: the so-called Tory Spartans who have never voted for any deal are folding, and new Labour rebels like Melanie Onn are finally putting up. Whether that adds up to the moment of parliamentary catharsis Johnson wants will depend on whether those Labour MPs take him at his word, or Letwin at his.

The great irony in both outcomes, of course, is that nothing will change in the short term whichever way MPs vote: though Johnson's deal is much harder than May's and could mean economic hardship in the medium term, voting it through means a standstill transition period. Voting it down – or voting for Letwin – means extended EU membership. In either scenario, Johnson can pursue electoral gain without immediately subjecting voters to major economic pain.

Patrick Maguire is the New Statesman's political correspondent.