Are these the last days of Brexit? Theresa May will pledge to take the threat of no deal “off the table” following a ministerial revolt. Three junior ministers have warned the Prime Minister that they will have no alternative but to defy the whip and vote for Yvette Cooper's amendment unless May changes course with an open letter to the Mail.

It’s true that Cooper’s amendment wouldn't remove the cliff edge but would merely involve extending the run-up. The reality is that as no deal is in no-one's interests, the United Kingdom would end up being granted an extension. The fear of the European Research Group – and the legitimate criticism of the Cooper amendment is – what on earth is going to change during the terms of the extension? And if the answer is “nothing”, doesn’t that just mean that transition will roll on and on until either the Conservative civil war is resolved or another party is able to command a majority of one kind or another in the House of Commons?

The Brexit deadlock stems, fundamentally, from the fact that this Parliament is almost perfectly engineered to be unable to resolve the Brexit crisis one way or another. There isn’t a majority within the governing party for any form of exit that can survive negotiation with the EU. There isn’t a majority within Parliament for a non-negotiated exit. There is, potentially, a majority in the House of Commons for a soft exit but there is no appetite for that in Downing Street.

What about sacking the whole thing off? Elsewhere, Jeremy Corbyn has thrown his weight behind a second referendum, saying that in the event that his Brexit proposals cannot command a Commons majority, Labour will support a public vote.

The reality is that official Labour support has always been a necessary, but far from sufficient, prerequisite to getting another referendum. There are 28 Labour MPs who have rebelled against the party whip to make Brexit harder. To get a second referendum through Parliament you need four more Conservative MPs to rebel than Labour – so the minimum number is 32, more than the total combined number of Conservative MPs to vote against the whip to make Brexit softer (a number which includes many vocal opponents of a second referendum). As Tony Blair conceded in conversation with the Spectator's diary columnist Steerpike, “the parliamentary arithmetic is pretty complicated.” That hasn't changed.

What has really changed is that the electoral trade-offs from Labour's perspective have shifted, to one where the considerable electoral risks of moving to a second referendum position are outweighed by the consequences of not moving to a second referendum.

That's the main reason why people are being too clever-clever in looking at ways that Labour's pledge might not really, truly be a commitment to another referendum. The strategic call is that Labour cannot allow itself to be outflanked on this issue by the Independent Group. (Given the pattern in the polls and the seats they need to win for majority government there's an equally strong, perhaps stronger, case that they cannot allow themselves to be outflanked in Scotland by the SNP and in Wales by Plaid Cymru too, but that's a question for another time.) That is not going to change and it moves Labour to a position they would rather not be in on a second referendum.

But ultimately that change doesn't matter at all unless a large number of Conservative MPs come round to a referendum as the only way to resolve the crisis without turning to the electoral event they want even less: a general election with May still at the helm and Brexit unresolved.