Why am I confident of that?
Well it is the last possible date for the contest that the shop stewards for Tory MPs, the executive for the 1922 committee, deem acceptable.
And - perhaps more importantly - it is the date that the PM has signalled to her closest allies that she can tolerate.
Well she does not want the state visit of Donald Trump and the D-Day celebrations of the preceding week to be undermined by the unseemly spectacle of Tory MPs and ministers scrabbling and scrambling to replace her.
I expect all of this to be settled tomorrow morning between Theresa May and the chairman of the 1922 committee, Sir Graham Brady.
And my assumption is the PM will announce this timetable for her departure today.
Truthfully the PM has no choice but to set an unbreakable date for her departure. The threat from the '22 is that if she were to dig in, they would hold a no-confidence vote about her fitness to continue at the start of Trump's visit, on 4 June.
The humiliation for her of being publicly rejected by her own MPs in plain sight of the US president would be too much for her to bear, surely.
It is also conspicuous that she has lost the confidence of her cabinet. As pressure on the PM to go intensified yesterday, and Andrea Leadsom quit as leader of the House, not a single minister came out to defend her.
"Cabinet won't function unless she names a departure date" one minister told me.
So the deal on her resignation is - in effect - done.
There is something else the '22 and Tory MPs are insisting on - which is that May formally kills the Withdrawal Agreement Bill (or WAB) and any intention of holding indicative votes on what kind of future relationship with the EU is acceptable to MPs of all parties.
May will be reluctant to do this, having invested her entire being in delivering her own version of Brexit.
But maybe, when members of the '22 executive talk to their friends in the cabinet, they will learn the WAB is effectively dead - because it won't be supported by ministers in its current form, and there is no consensus on how to amend it.
So perhaps they will soften their demand that she personally has to drown the WAB at birth.
All that said, even after tomorrow we won't quite know when we'll have a new PM - because the Conservative Party Board will have to decide at what point Tory members will vote to pick the new leader from the duo who will have been chosen in a ballot of MPs.
The '22 wants the new leader in place before the summer recess - but that means the whole election process will have to be very speedy and completed by around 13 July, to give the new PM the ability to test whether he or she enjoys the confidence of parliament.
If the contest can't be done by then, it would have to run over the summer - with the ballot of members concluding in early September.
But delaying till then will be seen by most Tory MPs as giving the new PM too little time to make their mark before the (new) historic date for the UK's departure from the EU on 31 October.
May herself would presumably prefer September for her own exit from 10 Downing Street (Mayxit or Terexit?) though I doubt she will have that luxury.
That said, she is desperate - I am told - to rush through pet projects and legislation before the removal men arrive. Her residual hope is that she can be remembered by history by a moniker other than as the PM who tried and failed to deliver Brexit.