Theresa May is under pressure to get an agreement from the Democratic Unionist Party (DUP) on the status of the Irish border when the UK leaves the EU, BBC reports.
The prime minister pulled out of a deal with Brussels that would have kick-started trade talks after meeting fierce resistance from the DUP.
The party said it would not accept a deal which saw Northern Ireland treated differently from the rest of the UK.
Mrs May is due to update ministers at a cabinet meeting on Tuesday morning.
Former Brexit minister David Jones described Monday as a "very difficult day" and said the prime minister now had "a lot of talking to do" with DUP leader Arlene Foster.
He believed the DUP had been spoken to beforehand about what was being proposed, but that the precise wording had not been explained and the Northern Ireland party "clearly thought twice".
Mr Jones, one of the Eurosceptic MPs on the Conservative benches, said he too was not happy with the key phrase the DUP objected to in the draft agreement, which apparently guaranteed "regulatory alignment" between Northern Ireland and the Republic of Ireland.
The prime minister needs the support of the DUP, which is Northern Ireland's largest party and has 10 MPs at Westminster, because she does not have a majority to win votes in the House of Commons.
Former top Foreign Office official Lord Ricketts said the row was "damaging" for Mrs May, adding that it was "pretty extraordinary that this wasn't all stitched up with the DUP beforehand".
"We're used to prime ministers going to Brussels and having a row with the EU and coming back without an agreement, but to go to agree with the EU and then have a row on your own side is inconvenient," he said.