David Davis, the Brexit Secretary, and arguably the most important minister in this Government other than the Prime Minister, faces a moment of truth on Thursday.
He is completely clear that it would be a disastrous mistake for the Prime Minister and the UK Government to offer Brussels a backstop proposal for keeping the Irish border open that does not contain a specified end date.
His reason is simple.
That backstop would commit the UK to staying in the customs union and single market.
And once the EU were to have that commitment, Davis believes - plausibly - that his Brussels interlocutor Michel Barnier would no longer have any incentive to negotiate seriously on alternative arrangements for keeping the border open.
Davis would have zero leverage in those talks to obtain technical or fiscal solutions to the border issue.
And since Davis takes the view that a backstop without an end date would leave him with no bargaining chips, it is very difficult to see how he could stay in his job.
But there is no sign of the PM and Downing Street backing down to give him what he wants.
My Downing Street sources tell me that it is impossible to write a date into the backstop, simply because it is impossible to know how long the backstop would be needed.
And they are also saying that we are likely to see the finished backstop on Thursday - though whether it will be published before or after the Brexit war cabinet meets (also on Thursday) is unclear.
For the avoidance of doubt, May and Downing Street are well aware that Davis has become more and more disillusioned about how they are backseat driving the Brexit negotiations - in a manner he sees as delivering sub-optimal outcomes (to put it euphemistically).
But they don't seem too bothered.
So will Davis quit on Thursday? I would not bet anything valuable on him choosing to stay.