Once there are two Tory MPs left Conservative party members can select one of them to become Prime Minister.
If she loses, she must resign and a party leadership contest is held in which she is barred from running.
The pound, which has lost 25 cents against the USA dollar since the 2016 referendum, fell again amid reports that Mrs May would face a leadership challenge. "The Prime Minister has lost her majority in Parliament, her government is in chaos and she is unable to deliver a Brexit deal".
Oxford East Labour MP Anneliese Dodds said: "This is putting the interests of quite a small number of people first, who have quite extreme views, and putting them before the interests of British business, our universities and all the European Union citizens who are based here".
One cabinet minister said that the PM had tried to reassure MPs that she would not do anything to break faith with the DUP.
They want assurances that the Commons will be given sufficient time to debate the Government's negotiating objectives.
"She believes it is her duty to serve as long as the party wants her to".
May had been scheduled to appear in the House of Commons on Wednesday for a regular question-and-answer session with MPs.
With time running out until March 29 when the United Kingdom is due to leave the EU, European leaders however have warned that the EU deal is not up for renegotiation, though the European Court of Justice confirmed Britain could unilaterally cancel Article 50.
Any such undertakings would be "completely irrelevant" if they were not included in the withdrawal agreement, MP Jacob Rees-Mogg, a leading Brexit supporter, told reporters.
She added: "We must and we shall deliver on the referendum vote and seize the opportunities that lie ahead".
Under party rules, if 15 per cent of Tory members of parliament write to the chairman of the backbench 1922 committee expressing no confidence in their party leader, then a ballot is triggered.
Brady said the vote would be held in Parliament between 6pm and 8pm Wednesday (7am and 9am Thursday NZT), with the results announced soon after.
Immediate statements of loyalty for the Prime Minister were issued by every MP in Cabinet, including several who have been touted as possible successors.
THERESA May's time in Number 10 could be coming to an end after Tory MPs triggered a vote of no confidence.
"We are now actively, not only preparing for that, but taking actions to ensure that if necessary we will be ready on March 29 for Britain to leave the European Union without a deal", Mr Coveney told Irish national broadcaster RTE, adding that he still thought a no-deal Brexit was unlikely.
May has repeatedly said that British lawmakers face a choice of approving her deal or facing an exit with no deal or even the reversal of Brexit.
Tory Brexiteers are increasingly confident they have enough support to trigger a no-confidence vote in Theresa May as party leader.
Indeed, there have been suggestions that if she made clear to colleagues at the 1922 Committee this evening that this would be the case, then that might bolster her ballot numbers in the confidence vote; people would know her own period in Downing St would be over by the spring.
"The last thing our country needs right now is a Conservative Party leadership election", Mr Javid said.
A new leader could not be in place by the January 21 deadline by which the PM must confirm an agreement in principle had been reached with Brussels on a Brexit deal, she said.