Can the DUP prop up a short-dated prime minister?

I've never known anger directed by MPs towards a party leader as that expressed to me by Tories against Theresa May.

Of course, the contempt in which most Labour MPs held Corbyn just a few months ago was almost as acute.

But the difference between Corbyn and May is that Labour MPs could see no way to get rid of him - because the party's members were apparently still behind him.

By contrast, Tory MPs know that she serves only at their pleasure. And she confirmed as such to them in her meeting with them just over a week ago.

At the moment their pleasure extends no later than July 20, when they go off for their summer break.

But there are no guarantees for her after that.

And they will spend the summer recess weighing whether the disruption of choosing yet another leader not much more than a year after her coronation is more damaging than the erosion of confidence in their party and "brand" by the continued presence of a prime minister who is seen to have lost her touch.

DUP leader Arlene Foster and MP Nigel Dodds at Downing Street Credit: PA

So if you want to know why the DUP is dragging its feet on the announcement of a deal to prop up her government, which to all intents and purposes was agreed last week, one reason is that the deal is with her, not with the Tory party.

And DUP MPs are hearing from their Tory chums exactly what I am hearing, that any agreement with her may be of extremely short duration.

Which poses something of a tricky problem for Arlene Foster, the DUP's leader - whose first responsibility is to her own party.

Does she want to be seen to be sustaining in office a party leader, May, whose own MPs are openly debating the best moment to replace her?

What does it do for the DUP's image, especially with its own supporters in Northern Ireland, to be giving a lifeline to a rival party leader whose authority within her own party has been eviscerated?

I assume the deal between DUP and May will be announced tomorrow, because failure to do so would push May to the very brink of oblivion.

But with her fate hanging on the whim of 10 DUP MPs, her grip on power is tenuous - as if you needed telling.