Speculation has grown about the concept of a "Plan B" - the path May will choose to take if her withdrawal agreement is voted down in parliament. Evidence of that tactic emerged nearly immediately on Sunday, with Tory Chairman Brandon Lewis saying that "the best way to prevent" that outcome is to "get this deal through Parliament on December 11". What does that mean exactly?
"You would need the government to actually table a proposal, have a vote in favour of it, which would require cross-party support", Nick Wright, a fellow in European Union politics at University College London, told AFP.
"A lot of work has gone into this, but I think the key thing is focus on the end point, and delivering what people voted for".
May gave the evasive reply: "Formally what happens if the vote doesn't go through is that the Government has to come back to Parliament within a certain amount of time and say what the next step is".
Attorney General Geoffrey Cox will also reveal to MPs highly-anticipated legal advice on the Brexit backstop.
Speaking on ITV's This Morning, the prime minister urged MPs to "hold their nerve" and get Brexit "over the line" - suggesting Parliament had a "duty to do what people asked us to do" by taking the United Kingdom out of the EU.
And Mr Gyimah, who until Friday was a science minister, said the government had a duty to "level with the public".
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Writing in the Sunday Telegraph today, Starmer said: "MPs must have access to the fullest possible information about what they are voting on".
The MP, who voted to remain in the European Union in the Brexit referendum, said that supporting the deal will only serve to set Britain up for failure. "Britain will end up worse off, transformed from rule makers into rule takers".
Next week's parliamentary vote on British Prime Minister Theresa May's deal will go ahead, Interior Minister Sajid Javid says, rejecting media speculation that the government might not go ahead with the vote because they could lose it.
Dominic Raab, who quit as Brexit secretary last month in protest against May's deal, told the Sunday Times: "The legal position is clear".
The two-part agreement includes the legally binding terms of the UK's departure and an ambitious but vague declaration about future relations between the two sides.
This will put May in a hard position as she attempts to lobby Conservative Party votes for her bill, while potentially having to reveal compromises over the so-called Northern Ireland "backstop" position which could doom it in the eyes of pro-Brexit MPs.