Ex-Universities and Science Minister Sam Gyimah likens the agreement to a soccer match where the opposing team is the both referee and rule-maker.
According to some estimates, Mrs May is facing a humiliating defeat on December 11 in the historic Brexit vote at the hands of up to 100 rebel Tory MPs.
The only group which will not sign the motion is the Scottish Conservatives.
Britain's Prime Minister Theresa May speaks during a meeting with Japan's Prime Minister Shinzo Abe at the G20 Leader's Summit in Buenos Aires, Argentina, Saturday, Dec. 1, 2018. His resignation came after May said Britain was abandoning efforts to retain full access to the EU's Galileo satellite navigation system after Brexit. Some opponents are calling for a second referendum now that the costs of leaving the European Union have become clear, but May says that would violate the trust of the 17.4 million people who voted for Brexit in 2016.
May said, given the EU's decision "to bar the United Kingdom from being fully involved in developing all aspects of Galileo, it is only right that we find alternatives".
"To fully debate only the Prime Minister's view and that of the leader of the Opposition - views which have been televised repeatedly in recent weeks, and which are simply different versions of Brexit, whilst positioning other options on the side of the debate, would be to prevent the public benefiting from a full understanding of the options and potential outcomes facing the United Kingdom as a whole and as a result would be a severe dereliction of your public duty". "We will be explaining to members of parliament why we believe that this is a good deal for the UK", May told reporters on the plane to the G20 summit in Argentina when asked if she had a back-up plan.
"Even before we get to new trade opportunities afforded by new trade agreements there are still considerable export opportunities for British businesses to exploit in existing markets", he said. "That is actually a betrayal of the British people".
Only a small group of Brexiter cabinet ministers are left to circle the wagons ahead of the crunch Brexit vote in December.
Researchers at IQR carried found 41 percent of the sample to prefer staying in the bloc, while just 25 percent though May's draft deal is the better option.
Under the Fixed Term Parliament Act, the opposition would have to win a vote of no confidence in the PM in the Commons and then hope the Conservatives could put together a Government which could win a second vote, in which case a general election would be called.
That could take the form of not leaving the European Union at all, or leaving with no deal - a state of affairs enthusiastically advocated by long-time Brexit campaigners like Nigel Farage and Jacob Rees-Mogg as a true Brexit which would leave Britain able to pursue its own destiny - but there would be no renegotiation.
Britain is expected to announce that it will create a post of trade envoy to Buenos Aires following talks between Mrs May and Argentinian President Mauricio Macri.