There were also continuing reports of a plan by senior Cabinet ministers who remain in Government to try to alter the withdrawal agreement at the 11th hour.
The European Union's chief negotiator Michel Barnier had held a press conference after the EU published the entire draft agreement on November 14, reaffirming that the "UK will remain our friend, our ally and our partner", after highlighting key clauses and protocols of the draft deal.
Elsewhere, Steve Barclay has been appointed the newBrexit Secretary, following Dominic Raab's resignation. But he did not answer when asked if he supported May's Brexit deal.
Last week saw the departure of Raab and the work and pensions secretary, Esther McVey, plus the launch by hardline Tory leaver Jacob Rees-Mogg of a high-profile insurrection on the backbenches to remove May from office. "But I now believe it is time she stepped aside".
More leading supporters rallied to May's support, with environment minister Therese Coffey saying in a radio interview Saturday that May would win a vote of no confidence very convincingly.
But May's party does not command a majority in the 650-member House of Commons, holding only 315 seats and relying on the support of the 10 DUP members of parliament to govern.
But it appeared that some MPs had withdrawn letters, because there was no immediate announcement from Sir Graham Brady, the 1922 Committee chairman who keeps a tally, that the trigger point had been met.
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The Prime Minister added: "Who are we here for?" "It is the future relationship that delivers on the Brexit vote".
"If you don't think the deal meets those tests, you have to vote it down".
Asked how he would vote today if he could, he said: "I don't know".
"What it will do is bring in a degree of uncertainty".
He said: "If we can not close this deal on reasonable terms we need to be very honest with the country that we will not be bribed and blackmailed or bullied and we will walk away". This is likely to be hard, as both its government partner, the Northern Irish Protestant party, the DUP, as well as many members of your own party don't want to support the present design.
Amid deep disagreements over the best way forward for the UK, May's proposal has remarkably appeared to unite politicians from across party divides in their droves.
May is sticking resolutely to her strategy in the face of widespread hostility from opposition parties, her supposed allies in Northern Ireland's Democratic Unionist Party, and members of her own Conservatives.
She said the backstop is an "insurance policy", adding: "Both sides can say yes we agree that there are arrangements in place, that a deal that provides for the people of Northern Ireland and therefore that backstop is no longer necessary". The risk of no deal is already causing economic harm as companies of all sizes stockpile goods and components and move jobs and investment out of Britain, it said.