The Prime Minister had hoped her deal, which opens up the possibility of a second referendum, would sway Labour to get behind it.
The backlash has been so bad that Michael Gove suggested this morning that the deal could be pulled
Refusing to confirm the vote would go ahead as planned in two weeks time, the Environment Secretary told BBC Radio 4's Today programme: "I think everyone should take an opportunity to reflect on what the PM will say later today and look at the Bill.
"I can understand the strong feelings - I have strong feelings - on leaving the European Union that have been aired and articulated over the course of the last 24 hours.
"We will reflect over the course of the next few days on how people look at the proposition that has been put forward."
Should the bill be pulled, Mrs May's early resignation would be much more likely.
European Research Group chairman Jacob Rees-Mogg also said that the PM should think again, following the backlash from MPs.
He added: "I hope that the Prime Minster will look at the figures, look at the lack of support for her deal, remember that she lost the first vote by 230 and the constitutional conventions and recognise that, in truth, the Prime Minister does not command a majority in the House of Commons.
"We see that with the lack of business in the House of Commons - the last Bill of any significance we've had before us has been on wild animals in circuses. The House of Commons is not functioning."
Mr Rees-Mogg suggested it would be "more dignified and more elegant" if Mrs May followed the constitutional convention of quitting if she lost the support of a Commons majority rather than relying on an internal Tory rule change to oust her.
Technically the PM is safe until December after she successfully thwarted a no-confidence vote against her last year but Tories are attempting to change the rules to remove her now.
Furious Brexiteer Nigel Evans said: "She has U-turned on absolutely everything. We cannot put up with this any longer.
"I will be asking my colleagues tomorrow to agree to a rule change so we can hold an immediate confidence vote if Theresa is not prepared to stand down now."
The PM has already met with the 1922 Committee of Tory backbench MPs who have demanded her to set out a definitive plan of when she will leave.
So far she has managed to delay stating her exit plans - but the possibility for a second referendum may have finally sealed her fate.
Some reports suggest the tipping point could come on Sunday and Monday, when the full scale of the Conservatives' expected disastrous performance in the European elections becomes apparent.
Tories were incensed at the latest proposals, with the deal being described as "dead on arrival" by Conservative Mark Francois, vice-chairman of the European Research Group (ERG).
Former Foreign Secretary - and favourite to be the next Tory leader - Boris Johnson said: "Now we are being asked to vote for a customs union and a second referendum. The Bill is directly against our manifesto - and I will not vote for it.
"We can and must do better - and deliver what the people voted for."
With great reluctance I backed MV3. Now we are being asked to vote for a customs union and a second referendum. The Bill is directly against our manifesto - and I will not vote for it. We can and must do better - and deliver what the people voted for.- Boris Johnson (@BorisJohnson) May 21, 2019
I listened carefully to the PM's speech on the govt's revised terms of Brexit. I cannot support legislation that would be the vehicle for a second referendum or Customs Union. Either option would frustrate rather than deliver Brexit - and break our clear manifesto promises.- Dominic Raab (@DominicRaab) May 21, 2019
It's simply not good enough to abdicate all responsibility for the type of Brexit we end up with. You are the Prime Minister. You can't stand there and say 'I do not support a second referendum, but Parliament would like one so I'll just go along with it'. You are meant to LEAD!- Ben Bradley MP (@bbradleymp) May 21, 2019
Former Brexit secretary Dominic Raab - another leadership hopeful - said: "I cannot support legislation that would be the vehicle for a second referendum or Customs Union.
"Either option would frustrate rather than deliver Brexit - and break our clear manifesto promises."
Things have got worse for May overnight - One MP who is putting a letter in hope of speeding up PM's exit says May had stopped meeting backbenches + stopped listening - 'she's a genius when it comes to making matters worse'- Laura Kuenssberg (@bbclaurak) May 22, 2019
There is a new push to oust PM asap so she doesn't have chance to put the bill forward being led by Nigel Evans - tory backbench cttee meeting today - one tells me 'it's Sunday' - day when euro results come thro that it's over- Laura Kuenssberg (@bbclaurak) May 22, 2019
In an astonishing attack on the PM, Tory MP Ben Bradley tweeted: "It's simply not good enough to abdicate all responsibility for the type of Brexit we end up with.
"You are the Prime Minister. You can't stand there and say 'I do not support a second referendum, but Parliament would like one so I'll just go along with it'. You are meant to LEAD!"
The Labour response
Mrs May has urged Labour leader Jeremy Corbyn to compromise and back her Brexit deal after the proposals received a hostile response from critics on her own side.
But, responding to the pleas for compromise, Mr Corbyn said: "We will, of course, look seriously at the details of the Withdrawal Agreement Bill when it is published.
"But we won't back a repackaged version of the same old deal - and it's clear that this weak and disintegrating government is unable to deliver on its own commitments."
It wasn't just Labour who refused to back the deal - Mrs May also failed to win immediate support from her DUP allies.
DUP parliamentary leader Nigel Dodds said: "We will examine the legislation closely when the Bill is finally published but the fundamental flaws of the draft Withdrawal Agreement treaty itself remain unchanged.
"Many of the proposals on the backstop serve as an attempt through domestic law to mitigate a bad deal, whereas the focus should be on getting a better deal."
The immediate future
Mrs May, who will face the Commons later today, is still hoping her 10-point compromise plan will woo enough Labour and DUP MPs to make up for Tory Eurosceptics who are implacably opposed to her deal.
But with a high chance of the deal being rejected again, the PM will face intense pressure to quit immediately.
Her position will only get worse in the coming few days as voters are set to punish the Tories in Thursday's European elections.
Nigel Farage's Brexit Party is set to win big, with polls showing a clear lead for the no-deal supporting group.
- This article first appeared on Yahoo
Read more from Yahoo News UK: