The Democratic Unionist Party, which props up Mrs May's administration, made clear it would not support the Government in a confidence motion if her deal survives.
But the party's 10 MPs will back the Prime Minister if her EU divorce plan, including the controversial Northern Ireland backstop measure, is rejected on December 11.
The DUP's position heaps further pressure on Mrs May ahead of the crunch vote on the Withdrawal Agreement and Political Declaration thrashed out after months of negotiations in Brussels.
Labour has indicated it will table a motion of no confidence in the Prime Minister in the wake of a defeat on such a pivotal issue for Mrs May.
Tory resistance to the Brexit plan could be bolstered by the knowledge that voting down the deal will not necessarily result in the collapse of the Government given the DUP's stance.
The DUP's Westminster leader Nigel Dodds said it would be "illogical" for his party to turn on the Tories if it had already seen off the Brexit deal.
The Government has gone to extraordinary lengths in an effort to limit the rebellion next week
Chief Whip Julian Smith attended a meeting with the European Research Group (ERG) of Brexiteers in Parliament on Wednesday night and was said to be in "listening" mode - although no concessions were offered to would-be rebels.
Meanwhile an ERG source said members of the Privy Council - senior MPs and former ministers - had been invited to a briefing with the Cabinet Office's Civil Contingencies Secretariat to be told about the potential impact of a no-deal Brexit.
The likelihood of defeat, and the further damage that will do to Mrs May's fragile authority, has led to some Cabinet ministers suggesting the vote should be postponed, The Times reported.
Debate on the Brexit agreement will continue in the Commons on Thursday.
Meanwhile The Daily Telegraph reported that Brussels could be prepared to discuss extending Article 50 - delaying Brexit until after March 29 2019 - if the deal is rejected by MPs.
The entrenched opposition faced by Mrs May on her own benches was made clear at the ERG's meeting in the Palace of Westminster.
The group's chairman Jacob Rees-Mogg, who had held talks with Mr Dodds earlier in the day, told the private meeting: "The DUP will support the Government in a confidence motion if the Withdrawal Agreement is voted down.
"But the risk of losing them and having an election is if the Withdrawal Agreement goes through."
Sources at the ERG meeting described it as "full and frank" and "candid", with the Chief Whip left in no doubt about what would be required to win over would-be rebels.
A Government source said the Whips' Office and the Prime Minister would do "as much as possible" to get support in "one of the biggest votes in recent parliamentary history".
The source said ministers were "looking at all options to secure the vote".
But it is understood that no detailed policy proposals were put forward by the Government at the meeting.
One potential measure reportedly being floated as a way to win over would-be rebels is a "parliamentary lock" which would give MPs a vote before the Northern Irish backstop is implemented.
But a senior Eurosceptic said the ERG had "seen no text for any amendment" other than those which had already been put down.
And Mr Dodds dismissed the "parliamentary lock", pointing out that "it doesn't have any effect" on the Withdrawal Agreement thrashed out with Brussels which contains the contentious measure.
On ITV's Peston, Mr Dodds said there would be "implications" for the Prime Minister if she pressed ahead with the deal.
"That's the risk that the Prime Minister is running," he said.
On BBC's Newsnight, Mr Dodds added: "I don't think a general election at this stage is in the interests of the country. I don't think a second referendum is either.
"I think Parliament has been given its instructions by the people of the UK as a whole to get on with Brexit."
He said that nobody wanted a no-deal Brexit but time had been wasted by the Prime Minister "going down a path that she must have known weeks ago couldn't command a majority in Parliament".