So at last, we really really really are entering the crunch phase of Brexit talks. You have heard this before but this time it is true.
Because the British government - not Brussels, not the EU27 leaders - has decided that unless there is a deal this month, the default option of a no-deal Brexit becomes the probable outcome.
"We don’t want no-deal. But because of the parliamentary timetable it becomes very hard to avoid if talks continue past this month" said a senior member of the government. "And that is why negotiations have massively shifted up a gear, with officials working through the night."
The important dates are tomorrow, when the prime minister briefs her cabinet on the likely shape of a deal, and (probably) next Monday - which is the probable cut-off day for organising an emergency Brexit council of EU leaders.
Or to put it another way, a week from today is when a comprehensive framework for withdrawal from the EU and the future relationship will need to have been settled, or preparations for a no-deal Brexit will have to be massively stepped up.
What are the obstacles?
The daunting one is the same as ever it was - how to keep open the border between Northern Ireland and the Republic.
Now the EU felt (rightly) it moved very significantly towards accommodating May’s sensibilities last week, by belatedly agreeing in principle that the insurance policy or backstop to avoid any border checks on the island of Ireland could include the whole UK staying in a customs union with the EU, and not just Northern Ireland - so as to prevent the creation of a UK-fracturing hard border between Great Britain and NI.
But it is not enough for May and her cabinet. And on its own, without associated constraints on the UK’s freedom to manage its economy, there remain problems and concerns for the EU27, especially France.
For example, a backstop that was only about avoiding tariffs being levied at Dover and Calais would still introduce friction at those ports - thus damaging British industries dependent on friction-less trade.
So May would prefer a backstop which also allowed for continued regulatory alignment between the UK and EU - such that British-based businesses with global supply chains did not risk falling off a cliff when the so-called Brexit implementation period, or our temporary status as a non-voting EU member, ends on 31 December 2020.
But to many Brexiters that would look like the UK as the EU’s vassal or enslaved state - since such a backstop would see the UK following EU rules for business, the environment and competition and having no right to agree free-trade deals with other countries.
And for many in the EU it would look like the UK having and eating that notorious cake.
So both sides, the UK and the EU, have an interest in making it crystal clear that the backstop cannot be forever.
Neither side wants the other side to have the unilateral right to end the backstop period - for the normal if depressing reasons of national and supranational pride.
There will have to be a dual control mechanism for deciding when the backstop is no longer needed.
Here is what will electrify UK politics and outrage many Brexiters.
The dual control mechanism will be seen by Brexiters as the EU27 having a right to veto any decision by the UK to terminate the backstop.
And they would be right. The EU will not agree any Brexit deal that does not give the EU27 the ability to overrule any request by the UK to exit from backstop arrangements.
So there will only be a Brexit deal if enough Brexiters can be persuaded to trust that the EU has no interest in keeping the UK in backstop arrangements forever - but reserves the right for legitimate reasons to assess whether the border in Ireland could be kept open by means other than the backstop.
In the short term, the risk for May of Brexiters cutting up rough is that a few members of the Cabinet may prefer to resign than endorse what they would see as backstop (the UK as vassal state) in perpetuity - and most ministerial eyes are on the Brexiter Brexit secretary Dominic Raab, because he has been publicly posturing that the UK must have a unilateral right to terminate the backstop.
"What none of us know is whether that is theatre for the benefit of [the Brexiter] ERG, so he can say to them that he did his best to rein in the PM" said one of his colleagues. "Or whether he is really on the point of quitting".
Another said: "The PM can probably get the Brexit deal she wants through the Cabinet but possibly not without saying goodbye to some colleagues. As I said, for a variety of reasons this is a big week".