"I will contest that vote with everything I have got," said Mrs. May on Wednesday, December 12.
If she loses she will not be able to stand in a leadership contest and will be a lame duck prime minister until the new leader takes over next month.
Who is best placed to take over?
The betting favourite (odds as short as 7-2 with online gambling website Bet365) is the MP for Uxbridge and South Ruislip.
Boris Johnson stabbed his old Etonian friend David Cameron in the back in 2016 by deciding at the last minute to back the Leave campaign ahead of the Brexit referendum.
He then stood for the leadership after Cameron resigned in the wake of the referendum vote but dramatically quit the race after his ally Michael Gove suddenly turned on him and publicly doubted his credentials.
Despite all that he remains popular with grassroots Conservative Party members and his reputation with them was not necessarily tarnished by his spell as Foreign Secretary despite a string of gaffes.
Johnson, 54, eventually resigned from the Cabinet in September this year
"We are truly headed for the status of a colony — and many will struggle to see the economic or political advantage of that particular arrangement," he said in a resignation letter calculated to damage May and her Brexit negotiations.
If he were to be elected as leader and become the prime minister Johnson would have to use all of his legendary charm to persuade EU leaders to change their stance on the Northern Ireland backstop at the last minute.
Mrs. May hoped he would be able to drive through a compromise with the EU after Davis' prickly personality and Leave stance failed to endear him to chief Brexit negotiator Michel Barnier.
Raab's constituency, Esher and Walton in Surrey voted 58.4 percent to 41.6 percent to remain in the European Union but he has not let that stop him speak out in favour of Brexit.
He was heavily involved in drafting the 585-page document which was finally agreed by May's Cabinet last month.
But the following day he quit, saying the deal had "two major and fatal flaws."
"The first is that the terms being offered by the EU threaten the integrity of the United Kingdom and the second is that they would lead to an indefinite if not permanent situation where we're locked into a regime with no say over the rules being applied, with no exit mechanism," Raab said.
His position has suddenly made him a key contender for the top job, despite his lack of experience and his apparent flip-flopping.
Javid — who replaced Amber Rudd as Home Secretary in April in the aftermath of the Windrush scandal — has been quiet on Brexit and kept his powder dry.
He has remained a loyal acolyte of Mrs. May and he may be rewarded for that in a leadership contest as acts of betrayal rarely pay dividends in politics.
If he were to be elected as leader the Conservative Party would claim a major first — he would be the first British prime minister from an ethnic minority.
Considering ethnic minorities traditionally vote for Labour, that would send a big signal to black and Asian voters.
But Javid — whose parents came to Britain from Pakistan — has to win first.
He studied politics and economics at Exeter University, where he was known as an admirer of Margaret Thatcher.
He became a Vice President at Chase Manhattan Bank at the tender age of 25 and later moved to Deutsche Bank in London and worked on emerging markets.
Javid is a rich man. He reportedly earned up to £3 million (US$4.1 million) a year during his 20-year banking career and now owns a £4 million (US$5.5 million) home in Fulham, a £3 million (US4.1 million) home in nearby Chelsea and sends his children to private schools.
Gove, 51, was born Graham, rather than Michael, to a young single mother in Edinburgh and was given up for adoption.
The Goves, who adopted him, lived in Aberdeen and his father ran a fish processing business but young Michael was sent to private school and grew up with a distinctly non-Scottish accent.
He went on to Oxford and then worked as a journalist before becoming an MP in 2005.
Hugely intelligent, Gove lacks the charisma and popular appeal of Johnson and has made plenty of enemies in the party, so he is not therefore seen as a likely winner.
In the 2016 leadership election Gove only won 48 votes and was eliminated after the second ballot.
He was widely seen to have paid the price for his betrayal of Boris Johnson.
In many ways Leadsom is a carbon copy of Theresa May and for that reason she may not be chosen as the next leader.
Born in affluent Buckinghamshire and educated at a grammar school, Leadsom attended Warwick University before entering the world of banking and was a fund manager at Invesco Perpetual before becoming an MP.
She backed the Leave campaign in the 2016 referendum and when Cameron fell on his sword she emerged as a dark horse contender for the leadership.
Leadsom polled more votes than Gove, Liam Fox and Stephen Crabb and was all set for a head-to-head contest with Mrs. May until she made a fatal blunder.
She gave an interview to the Sunday Times in which she appeared to say that the fact she was a mother gave her the edge over Mrs. May, who is childless.
Despite claiming her remarks had been taken out of context, Mrs. Leadsom bowed out of the contest, leading to Mrs. May becoming leader and prime minister.
Mrs. Leadsom was forgiven by Mrs. May and became Leader of the Commons.
Hunt was deeply unpopular with nurses and doctors — and arguably with patients — during his spell as Health Secretary.
But managing the NHS is a tough gig and Hunt was perceived within the Conservative Party as having made a good fist of it and was rewarded by Mrs. May by being promoted to Foreign Secretary when Boris Johnson resigned.
One of his first jobs was to visit China in July and while there he married a gaffe which received widespread publicity.
"My wife is Japanese — my wife is Chinese. That's a terrible mistake to make," said Hunt during a meeting.
Hunt's wife, Wang Yi, is indeed Chinese and her parents still live in the ancient city of Xian.
If Hunt were to become Prime Minister he would no doubt use all his connections to try and improve Anglo-Chinese trade.
Jacob Rees-Mogg is the chairman of the European Research Group (ERG), a wing of the Tory Party which is fiercely opposed to the EU and wants a hard Brexit.
He has been deeply critical of Mrs. May's leadership and her handling of the Brexit negotiations.
"I think the Prime Minister will lead the conservatives into the next election and if you find MPs privately who think that is a good idea in any number, I would be quite surprised," Rees-Mogg told an ERG meeting last month.
Rees-Mogg, MP for North East Somerset, is proud of his plummy accent and his aristocratic background.
One of his children is called Anselm Charles Fitzwilliam Rees-Mogg and another is the splendidly monikered Sixtus Dominic Boniface Christopher Rees-Mogg.
He is a strong supporter of the monarchy and the Church of England and has opposed same sex marriage and abortion.
After resigning as Home Secretary in April, it would be a remarkable comeback if Rudd were to become Prime Minister.
Rudd, 55, quit after bungling the handling of the scandal of Caribbean immigrants — the so-called Windrush generation — being deported from the UK despite living and working in the country for many years.
Another problem Rudd faces is that she represents Hastings, a marginal constituency which she only held onto last year after a recount.
If she were to become Tory leader it is more than likely she would be moved to a safer constituency, such as Mid-Sussex, rather than risk losing her seat at the next General Election.
Rudd was a Remainer before the Brexit referendum but is seen as a unifier and, despite her handling of the Windrush scandal, has many admirers within the Tory Party.
Born in the Labour heartland of Rotherham, South Yorkshire, and hailing from a family of steel workers, Greening comes from a very different background to the rest of the contenders.
She also became the first openly gay woman Cabinet minister when she came out in 2016.
Greening, 49, was promoted by Mrs. May to be Secretary of State for Education but resigned in January after reportedly refusing a sideways move to the Department of Work and Pensions.
As an MP for Putney in south-west London, she has long opposed the expansion of Heathrow Airport, a position which would be very difficult to maintain as Prime Minister.
She is a Remainer and is well-regarded for her integrity but may be unable to get enough support to beat Johnson or Raab in a leadership contest.
Mercer, is 37 and was only elected in 2015, so perhaps his time will come further down the line.
Davidson is not even an MP — she is the leader of the Scottish Conservatives and an MSP at Holyrood.
Odds of 500-1 are being offered on Farage, who recently quit UKIP.