So, the endgame then. For the last year the DUP have been supplying the Government with anything but confidence. The June 2016 sweetheart deal was horribly misnamed.

Now, finally, the DUP has called time on the Conservative government's obfuscations and ambiguities.

Equally, Theresa May has begun to call time on the DUP, whilst pretending otherwise.

The Prime Minister's leaked letter to the DUP insists that 'she could not accept there being any circumstances or conditions in which that "backstop to the backstop" which would break up the UK customs territory, could come into force'.

The UK would remain a single customs unit, temporarily aligned to the EU.

Did the PM really expect the DUP not to notice the absence of a similar guarantee to Northern Ireland regarding regulatory territory?

Dominic Raab might forget about Calais to Dover. Arlene, Nigel and Sammy were never going to do likewise for Stranraer to Larne.

For the DUP, the position is clear. If Theresa May really believes the exercise of a backstop, or a backstop to a backstop, cannot or will not happen on her watch - why sign up to a deal which keeps the possibility, however remote, of it happening?

And the possibility of a prolonged backstop is not remote at all. The chances of concluding an all-encompassing deal with the EU sometime soon seem about as good as those for an early restoration of the Stormont Assembly.

So a backstop moving from temporary to semi-permanent status is probable. And for the DUP any 'Northern Ireland only' backstop feature remains as untenable as it was a year ago.

The DUP position has some logic in terms of the party's own worldview - in which economics and constitutional issues are intertwined.

In a week in which Canadian economists have hailed the potential value of an all-island economy in a United Ireland, the DUP has again stressed the value of the UK single market.

And the DUP steadfastly refuses greater alignment with Ireland which risks Irish unity.

What, after all, if unionists get to like the dual trading arrangements of the supposed EU protectorate - a single EU market trading healthily across the border and the rest of the EU states - plus a largely unchanged UK single market?

They might dilute or even desert a unionism which is struggling demographically, politically and ideologically.

Whether, in terms of objective economics or constitutional analysis, the DUP's position makes sense is another matter.

There is no irrefutable evidence that a small increase in regulation of trade between Great Britain and Northern Ireland will diminish that trade.

A more politically dexterous DUP leadership might be less concerned with a modest extension of regulatory checks on goods travelling between Great Britain and Northern Ireland. There is already online documentation for the transit of such goods. As for the constitutional question, Northern Ireland's status within the UK is determined by the consent principle of the Good Friday Agreement, not by any one of Barnier, May or Varadkar.

But the DUP can hardly row back now.

What Theresa May is offering is unsellable in its present language even if the Prime Minister turns up on bended knee at the DUP conference two weeks from today offering another billion pounds.

So what can the DUP do, other than rage?

It's the Labour 257 (minus a few outright Brexiteers like Kate Hoey) who may matter far more than the DUP 10. If the Prime Minister can soften Brexit sufficiently - and a Customs Union plus an EU Single Market for Northern Ireland is on the cushioned landing side perhaps - then Labour might, just might, abstain or even back the government.

That's possibly a bigger ask than the Labour leadership remembering all six of their supposed Brexit "tests".

But Labour acquiescence would mean DUP irrelevance in terms of the parliamentary voting arithmetic.

If Labour rejects the government's proposals, the DUP parliamentary vote remains important.

Conservative Brexiteer opposition (too soft a withdrawal) plus DUP antipathy (Northern Ireland's position is paramount) plus hostility from all the other parties (Brexit seen as disastrous) means no parliamentary majority for the government proposals.

That in turn probably means (a) back to Brussels for a better deal - good luck with that; (b) general election - a snap election having worked out so well for the Conservatives last time; or (c) a so-called People's Vote.

And with that last option there is the possibility that the Brexit that 70% of DUP voters chose in 2016 doesn't happen at all ...

Jon Tonge is Professor of Politics at the University of Liverpool

Belfast Telegraph