The fragile alliance keeping the Prime Minister in power has been strained as the Democratic Unionist Party railed against measures it fears will create a border down the Irish Sea between Northern Ireland and the rest of the UK.
"I was in Dublin a few days ago".
That would include both a withdrawal agreement, governing the terms of Britain's exit, and a political declaration about the future trading relationship the two sides hope to negotiate after Brexit.
"The government will not agree anything that brings about a hard border on the island of Ireland".
Appearing on the Matthew Wright show, Mick Fealty, the editor of Northern Ireland-based political blog, Slugger O'Toole, said Irish businesses were anxious.
"I am clear that I could not accept there being any circumstances or conditions in which that "backstop to the backstop", which would break up the United Kingdom customs territory, could come into force".
The Irish government did not want to see any new borders between Ireland and Northern Ireland, he said, and that the point of the backstop, which in some forms the DUP opposes as it could lead to the separation of the United Kingdom and Northern Ireland, was to protect an open border.
But she acknowledged that the "unique circumstances" of Northern Ireland "could require specific alignment solutions in some scenarios" on regulations.
Downing Street reiterated the PM's own commitment to avoiding a hard border.
The letter, seen by The Times of London, was in response to a letter sent by the DUP to May on 1 November and suggests the European Union is looking for a customs border in the Irish Sea between Northern Ireland and the rest of the UK.
DUP Brexit spokesman Sammy Wilson told Sky News that Ms.
Foster said the British Prime Minister now has to decide if she wants to push forward with this proposal without the support of the 10 DUP MPs.
The UK government has so far proposed a backstop - with an expected end date of 2021 - which would effectively keep the whole of the UK in the EU customs union for a limited period after Brexit.
As we enter the endgame of the Brexit negotiation process, all pro-Remain parties must continue to represent the demand for our rights and political processes to be protected and the onus is firmly on the Dublin Government and the European Union 27 to ensure Theresa May is held accountable to the agreement she made in December. "If she continues down the road of bringing something forward which is unacceptable to a large part of her own party and ourselves, then I think the inevitable outcome is that it will be voted down in the House of Commons", Wilson told Sky News.