The deal believed to be on the table involves keeping the whole United Kingdom in an "arrangement" that effectively preserves the existing EU customs union, ensuring the goods continue to move freely over the Irish land border regardless of the future trade relationship between London and Brussels.
Cabinet big-hitters including foreign secretary Jeremy Hunt, Brexit secretary Dominic Raab, environment secretary Michael Gove and trade secretary Liam Fox are said to be ready to quit over the row.
The second part of the plan would see Northern Ireland stay in both the customs union and the EU single market.
"He said: "[The backstop] would have to be finite, it would have to be short and it would have to be, I think, time-limited in order for it to be supported here.
With the negotiations coming to a head, the central focus of the discussions is thought to have been the issue of the Northern Ireland "backstop" meant to ensure there is not return of a "hard border" with the Republic.
First, the good. Michel Barnier, the EU's chief Brexit negotiator, gave a speech saying that a deal could be done as early as next week.
El petróleo Brent baja un 0,29 %, hasta 83,82 dólares - Empresas
Así, los dirigentes de Total y British Petroleum negaron estar multiplicando los proyectos y las inversiones. La mezcla mexicana de exportación, por su parte, cayó 2.06%, o 1.59 dólares a 75.77 dólares el barril.
The UK has said it would recognise EU-issued licences for up to two years, after which operators would have to apply to the UK regulator for a new licence.
"The prime minister is a unionist". Many of her cabinet colleagues have assured me of their Unionism.
Meanwhile, also on Friday and speaking in London following a hard informal meeting of cabinet ministers in Downing Street, Mr Raab admitted the backstop issue is the "one real sticking point" in negotiations as he offered contradictory comments to Mr Coveney. "I believe that she should be insisting on the kind of deal with the European Union that she has been promising to people in the United Kingdom".
But even if her Brexit plan survives the meaningful vote, MPs could still insist the public be given a final say.
He told the BBC's Political Thinking podcast: "Their behaviour was pretty intolerable, but not almost as intolerable as the way the present prime minister is being treated".