The prime minister’s frantic last attempt to persuade Northern Ireland’s DUP to back her third meaningful vote on Tuesday involves a promise that if the controversial backstop is ever triggered, Great Britain would adopt any new food and business rules that could be forced by the EU on Northern Ireland.

This is a high risk offer by Theresa May to NI’s unionist party – which has huge clout with her because without its votes in parliament her government would collapse.

As a minister told me, for the DUP to accept the offer it would have to trust that a future prime minister and government would honour the pledge – which cannot be guaranteed even if May legislates for such alignment (because any law can always be repealed).

May’s offer falls far short of the DUP’s demand that the EU must change the so-called Withdrawal Agreement, to remove the potential for business and food regulations between Great Britain and NI to diverge – and thereby, according to the DUP, create a new kind of legal border between NI and the mainland.

It also risks alienating some Brexiteer purists because it would keep the whole of the UK tied to the EU’s single market and undermine further the ability of Westminster to – in their words – “take back control”.

What is perhaps worse and would rub salt into Brexiteer wounds, this unilateral British acceptance of alignment with EU rules, for as long as the backstop is in force, would not remove the responsibility of EU institutions to routinely interfere in UK affairs, to check that goods and food flowing from GB to NI meet EU standards.

So logically the regulatory alignment offer should not pacify and win over the DUP.

But sources close to the DUP tell me that – to their surprise – it may have done.

If so they would announce this entente as soon as tomorrow.

And as I said yesterday, the PM will not risk trying to win support from MPs for her Brexit plan with an unprecedented third meaningful vote unless and until the DUP publicly commit to back the deal.

Robert Peston is ITV’s Political Editor. This article originally appeared on his ITV news blog.