Lawmakers who believe it either leaves Britain too close or too distant from the bloc, fired ominous warning shots this week, voting to force the prime minister to quickly set out an alternative plan for Brexit if she loses the vote.
With her agreement facing nearly certain defeat in a House of Commons vote on Tuesday, May will make an 11th-hour appeal with a warning that there's now more chance of members of Parliament blocking Brexit than of Britain leaving the European Union without a deal.
"I think parliament is very committed to try to stop no-deal, but I think we have to recognise that there is a deal on the table, it does broadly deliver the Brexit people voted for, and if we don't find a way to get this through, we are taking some very big risks".
"People's faith in the democratic process and their politicians would suffer catastrophic harm", she will say.
Theresa May will liken Brexit to referendums on devolution in Scotland and Wales in a last-ditch appeal to MPs to respect the will of the people and ensure the United Kingdom leaves the EU.
Her choice of Stoke is significant.
Asked during an interview on BBC TV about the possibility of a second Brexit referendum, Corbyn said: "My own view is that I would rather get a negotiated deal now if we can to stop the danger of a no-deal exit from the European Union on 29 March which would be catastrophic for industry, catastrophic for trade".
Speaking on BBC radio, Mr Hunt said: "If this deal is rejected, ultimately what we may end up with is not a different type of Brexit but Brexit paralysis". According to Bank of England analysts, such a chaotic split could hammer the pound and house prices and plunge Britain into a recession worse than the financial crisis a decade ago.
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Reports from Westminster suggest more than 200 of the 650 MPs back the deal, far short of the number needed for it to pass.
Mrs May's minority government, which is propped up by a small Northern Irish party, was last week defeated twice in Parliament on Brexit, with lawmakers creating a new obstacle to a no deal Brexit and forcing Mrs May to promise she would come up with a "plan B" within days if her deal is rejected. His chance of victory is slim, however, and failure would put him under pressure to back the growing cross-party calls for a second referendum.
"Clearly if Theresa May's Brexit deal is voted down and clearly if a General Election takes place and a Labour government comes in - an election would take place in February/March time - clearly there is only a few weeks then between that and the leave date".
But May is facing an uphill task to save her withdrawal agreement - forged during 18 months of talks between London and Brussels - from a crushing defeat in parliament.
A margin of defeat exceeding about 60 lawmakers would probably mean the agreement is close to death and negotiations are in uncharted waters, several European Union officials said.