The warning comes amid reports that Cabinet ministers have told Mrs May the only way she will get her deal through Parliament is if she agrees to stand down by June.
Steve Baker, the deputy chairman of the pro-Brexit Tory European Research Group, and DUP deputy leader Nigel Dodds said without concessions from Brussels the Prime Minister will face another crushing Commons defeat.
On Tuesday, the Prime Minister will again ask MPs to back her Brexit deal, but if they reject it they may get a chance to vote to delay Brexit.
The UK is due to leave the EU on March 29.
Mr Baker and Mr Dodds warned that if that happened, it would cause “incalculable” damage to public trust in politics.
“For some, democracy would be effectively dead,” they said.
The Prime Minister had been pinning her hopes on securing legally binding changes to the backstop to convince MPs that the UK cannot be tied indefinitely to EU rules against its wishes.
An RAF plane is reported to be on standby to fly her to Brussels to clinch a deal if an agreement is in sight.
But with time running out, the chances of that happening appeared to be receding.
In a joint article for The Sunday Telegraph, Mr Baker and Mr Dodds described the situation as “grim” and warned that after January’s 230-vote defeat in the first “meaningful vote”, Mrs May appeared set for another heavy reverse.
“An unchanged Withdrawal Agreement will be defeated firmly by a sizeable proportion of Conservatives and the DUP if it is again presented to the Commons,” they wrote.
“If with the DUP just half of previous Conservative opponents vote against the deal, a three-figure majority would be expected.”
There had been speculation that if Mrs May could get the majority against the deal down to below 50, she could try to bring it back for a third “meaningful vote” – but another three-figure reverse would make that difficult.
Meanwhile Attorney General Geoffrey Cox has said he will not change his legal opinion on the backstop unless he is convinced there is no longer a risk the UK can be trapped in it indefinitely.
In his original legal advice, drawn up last November, Mr Cox said that under the terms of the backstop, the UK could be trapped in “protracted and repeated rounds of negotiations” for years ahead.
Since then, Mr Cox has taken a leading role in the Government’s efforts to secure changes to the backstop, leading some Tory Brexiteers to warn he will be “marking his own homework” when he comes to give his legal opinion on them.
However he told The Mail on Sunday: “I will not change my opinion unless I’m sure there is no legal risk of us being indefinitely detained in the backstop.
“I am putting my hand on my heart. I will not change my opinion unless we have a text that shows the risk has been eliminated. I would not put my name to anything less.”