A DUP source told Sky News: "It is unacceptable that we would be treated differently to the rest of the UK".
The ex-Brexit secretary issued his stark prediction in a letter urging all Conservative MPs to back a loose free trade deal with the European Union, rather than the PM's Chequers compromise proposals.
"If we stay on our current trajectory we will go into the next election with the government having delivered none of the benefits of Brexit, with the country reduced to being a rule-taker from Brussels, and having failed to deliver on a number of promises in the manifesto and in the Lancaster House speech", he wrote. "The electoral consequences could be dire".
"So it is in both the party's interest, and crucially the national interest, that we reset our negotiating strategy immediately and deliver a Brexit that meets the demands of the referendum and the interests of the British people".
Just six months before Britain is due to leave the European Union, the two sides differ on their view of the talks - the bloc says a withdrawal deal is within reach, while British officials say "big issues" still lie in the way of any agreement. "There can be no withdrawal agreement without a precise future framework".
The backstop is the insurance policy for making sure the frictionless border between Northern Ireland and the Republic is maintained after Brexit.
"I believe that is a very unlikely scenario". That's certainly not where I want to be.
Ousted Guardians of the Galaxy director switches camps, tied to new DC Comics film
Let's just say, it.did not work as well as Gunn's curated approach to music in the Guardians movies, and leave it at that. Joss Whedon - who directed the first two Avengers films - made a similar move, although in very different circumstances.
But Downing Street would say only that the United Kingdom was working for a deal "this autumn", fuelling speculation that a special summit in November will be needed to hammer out an agreement on issues including the status of the Irish border.
DUP leader Arlene Foster has repeated her insistence that there should be no customs or regulatory barriers between Great Britain and Northern Ireland, and said she had made this clear to the British Prime Minister Theresa May.
Reports had suggested that deadlock over the so-called "backstop" arrangements for Ireland could be broken by permitting checks on exports from the mainland to the north, but not in the opposite direction.
His comments come as business leaders accused politicians including the DUP and the Northern Ireland secretary, Karen Bradley, of doing nothing to secure the region's already weak economy in the face of Brexit.
The EU's chief Brexit negotiator Michel Barnier said on Wednesday that although some checks can take place away from the border, those on live animals and animal-derived products would have to take place at the border.
Newsnight's Nick Watt said the Northern Ireland party would end its Parliamentary support for the prime minister if she agrees to anything that leads to additional checks between Northern Ireland and the rest of the UK. The war Cabinet last met before the Chequers plan was agreed, and Cabinet sources suspect a similar attempt to create a fait accompli on the backstop.