The person she most wants to sell the deal to is U.S. President Donald Trump because a trans-Atlantic trade deal has been held up as one of the greatest prizes of Brexit.
"If they can not look their constituents in the eye and say it is, they must vote this deal down and then hand the decision back to the people".
Mrs May also accused Labour of pushing the United Kingdom towards a damaging no-deal Brexit by seeking to block her deal without offering a workable alternative.
Becoming the seventh member of the Government to quit since Theresa May unveiled the draft Withdrawal Agreement, Mr Gyimah says the plan was "not in the British national interest" and that voting for it would "set ourselves up for failure" by surrendering "our voice, our vote and our veto".
Mrs May has said no, Labour says yes but only if it does not get a general election. People need to have some clarity about that...
I am writing in relation to the proposed BBC TV debate on Brexit to take place on Sunday 9th December and would like to raise a number of concerns with you at this point.
In a speech in Bristol, the trade secretary said that MPs needed to look beyond their current divisions and get on with delivering Brexit so that the UK's "independent trading future" can begin.
In a round of broadcast interviews in Argentina, where she is attending the G20 summit, Mrs May declined to discuss whether she might offer a Plan B if her deal is voted down on December 11, or whether defeat could mean her resigning or being forced out.
The claim is at odds with analysis by May's own economic advisers, who say Britain's best option would be to stay in the European Union. "What I see from Labour is an attempt to frustrate what the government is doing to deliver Brexit for the British people".
She added: "I think what we have seen revealed in numerous Labour Party's comments is that what they actually want is a general election, and that means they are not acting in the national interest, they are putting their narrow party interests first".
The decision to back a People's Vote was taken at a meeting of council leaders in Edinburgh today.
Asked about the situation back in the UK, Mrs May said: "The next nine days are a really important time for our country leading up to the vote on this deal".
"The bottom line is that we must not end up with a no deal by default".
She added: "The view I have had from farmers, employers and sector organisations and others in my trips around the country is that they recognise the importance of this deal and they support this deal".
Writing on his Facebook, the East Surrey MP said: "After careful consideration and reflection, I can not support the Government's deal and as such, I have tended my resignation as Universities and Science Minister".
Conservative MP Jacob Rees-Mogg, a staunch Brexiter who is one of the most vocal critics of the deal, said Friday that the government was trying to frighten people into accepting it with dire forecasts about the impact of leaving the European Union without an agreement.