With little more than 100 days to go until Britain leaves the EU, Downing Street have accused Labour Leader Corbyn of a political stunt and effectively dared them to try and unseat May.
Corbyn tabled a long-threatened but non-binding motion of no confidence in the Prime Minister, demanding she hold a meaningful vote on the Brexit Withdrawal Agreement before Christmas.
The Labour leader stopped short of bringing a motion of no confidence in the Government under the Fixed-term Parliaments Act (FTPA) which, if the opposition won, could trigger a General Election.
Mrs May looked likely to win a vote after Brexiteer critics in her own party and the DUP said they would back her.
But the Government would also have to allow Commons time for the confidence vote to take place this week and a Downing Street source challenged Labour to strengthen its attack.
“We won't allow time for what is a stunt.”
They said: "We won't allow time for what is a stunt. The FTPA applies if Labour wants to put down a motion under the terms of that."
Several reports suggest the Cabinet will discuss extending no-deal preparedness at its regular weekly meeting in Downing Street, which comes with 101 days to go until the UK is due to leave the EU on March 29.
The Prime Minister had said the Commons would have the chance to debate her Withdrawal Agreement in the week MPs return to Westminster after Christmas on January 7.
The crucial vote – which was postponed earlier this month to avoid a heavy defeat – will take place the following week.
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Mr Corbyn told Mrs May: "A responsible prime minister would, for the good of this country, put this deal before the House this week so we could move on from this Government's disastrous negotiation."
He said it was "unacceptable" to delay the vote and confirmed he was tabling a motion "that this House has no confidence in the Prime Minister".
The wording of the motion, targeted at Mrs May rather than the Government as a whole, would not trigger the process set out under the Fixed-term Parliaments Act which could eventually lead to a general election.
But Labour said it was clearly a confidence motion and should be allocated time for debate by the Government.
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A House of Commons spokesman said: "By established convention the Government always accedes to the demand from the Leader of the Opposition to allot a day for the discussion of a motion tabled by the official Opposition which, in the Government's view, would have the effect of testing the confidence of the House.
"It will be for the Government to determine whether to schedule time for debate on this."
After Downing Street said it would not allow time for a vote on the PM, Labour Party chairman Ian Lavery accused Theresa May of "running scared of Jeremy Corbyn's no confidence vote, just as she's running scared of the vote on her flawed Brexit deal".
Mrs May's plan for Brexit has torn her party apart – with a failed bid by Tory rebels led by Jacob Rees-Mogg to unseat her last week.
LABOUR: Jeremy Corbyn the party leader has threatened a vote no-confidence (Pic: EPA)
The smaller opposition parties have tabled an amendment to Mr Corbyn's no-confidence vote in Mrs May that they say would beef it up into a full confidence vote in the Government.
The SNP, Liberal Democrats, Plaid Cymru and the Green Party have backed the change, laid down on Monday night to trigger the legally binding FTPA provisions.
Meanwhile, a group of more than 50 business figures have called on the PM to back a second referendum to break the deadlock if she cannot persuade MPs to back her Brexit deal when the vote takes place next month.
Senior figures in the City including Sir Richard Sykes, the chairman of Imperial College Healthcare NHS Trust, and former Marks and Spencer chairman Lord Myners, have signed a letter, published in the Daily Telegraph, which suggests her deal is "impossible to resuscitate" and urges her to "take (it) to the British people".