David Davis has insisted any regulatory alignment would apply to the whole of the UK - and that it does not require membership of the Single Market.
The Brexit secretary today insisted the suggestion that "leaving one part" of the country in the customs union is "emphatically not something the UK government is considering".
"The presumption of the discussion was that everything we talked about applied to the whole United Kingdom," he said. "Alignment isn’t harmonisation. It isn’t having exactly the same rules. It is sometimes having mutually recognised rules, mutually recognised inspection – that is what we are aiming at.”
Davis said regulatory alignment referred to specific areas such as employment rights, animal welfare and food standards, and was possible to maintain from outside the Single Market and customs union.
"Mutual recognition and alignment of standards that does not mean the same standards but one that gives similar results," he said.
Yesterday, SNP leader Nicola Sturgeon, Welsh first minister Carwyn Jones and London mayor Sadiq Khan piled into the leaked proposals, arguing that Northern Ireland should not be a special case in what they claim amounted to continued membership of the Single Market. That argument was echoed this morning by Scottish Conservative leader Ruth Davidson.
Davis told MPs he was still confident a deal could be concluded before the end of this week - although 24 hours ago he had gone on record saying a deal could be done yesterday afternoon.
May is due to speak to Foster and Sinn Fein's Stormont leader Michelle O'Neill today in the hopes of greasing the wheels after she was forced to admit a deal could not be agreed yesterday after a last-minute intervention from the DUP.
This afternoon the party explained exactly why it had scuppered those chances, with deputy leader Nigel Dodds telling journalists he had only been given sight of the text "late morning" - and that the wording was not what had been agreed beforehand.
It had "far too much ambiguity and didn't actually nail down the need to be nailed down," Dodds said.
May is still hopeful she will be in a position to return to Brussels and conclude the agreement before the end of the week, but will be in Westminster at least until PMQs tomorrow afternoon.