Her cabinet is also against a second plebiscite, and the leader of the Opposition Labour Party, Jeremy Corbyn, isn't a big fan, either.
But after two years of bickering, confusion and uncivil war over what Brexit should look like, and as it has become clear that the version approved by the EU and May's Cabinet has little chance of passing Parliament, more and more people are wondering whether a second, "people's vote" might be the only thing to break the impasse.
"I didn't think it very likely, but now I'm beginning to wonder if it's the only exit out of a burning building," said Tim Bale, a professor of politics at Queen Mary, University of London.
A year ago, London bookmaker William Hill was offering 12-1 odds for a second referendum. Today, it's 1-1.
Adding to the chaos, no one knows which way a new vote would go.
For a long while after the 2016 referendum, public opinion on Brexit didn't change much. Many people doubled down on whatever position they'd taken and began to define themselves as "leavers" or "remainers".
But as the trade-offs of their decision have become more apparent, there's been a slight shift. Many polls show that, if the choice today were between leaving or remaining, a small majority of Britons would vote to stay.
Those inclinations have not been tested by a hard-fought, second campaign.
Some of May's allies see a potential second referendum as a chance to secure a mandate for her Brexit deal, to give it the endorsement that Parliament appears unlikely to grant.
Nick Timothy, a former top aide to May, wrote in the Daily Telegraph that with her deal "dead as a dodo" in Parliament, the only viable options are a super "soft Brexit," where Britain pursues for a trade deal with the EU like the one Norway has (which isn't that popular) or a second referendum.
Is May in such a jam that she might go back to the public?
She is famously stubborn, but she is also pragmatic and she has tried mightily to stay relevant — and employed. She knows her deal is very unpopular. If it loses in the House of Commons, she just might pivot and support a second people's vote.
"It would not surprise me at all if the Prime Minister were to say, my deal has been defeated, you know what, I still think it's the right deal for the country and I'm going to put it to the country in a referendum and then off we go," Hilary Benn, a Labour MP and and remainer and chair of the Brexit select committee, told the BBC.
The organised push for a second referendum has been coming from europhiles in London and the university towns, economists, a couple of peers in the House of Lords, journalists who believe the first vote was rigged, and others who think leaving one of the world's largest and richest trading blocs is a dumb idea.
The Labour Party's activists love the idea of a do-over. At the party's convention in September, delegates voted overwhelmingly to support a second referendum, despite the lack of enthusiasm from most of the party leadership.
In October, hundreds of thousands of people took to the streets of London to demand a people's vote on any Brexit deal. Organisers called it the second largest protest in London in the 21st century, after the massive demonstration against the Iraq War in 2003.
Pro-Europeans were thrilled last month when the Conservative MP and remainer Jo Johnson — the younger brother of Brexiteer Boris Johnson — quit May's Cabinet and threw his weight behind a people's vote.
"Given that the reality of Brexit has turned out to be so far from what was once promised, the democratic thing to do is to give the public the final say," Jo Johnson wrote in his resignation letter.
The movement got a further boost when the European Court of Justice ruled that Britain could unilaterally reverse itself and stay in the EU if it chose to.
The path to a second referendum wouldn't be easy, though.
There isn't a majority in Parliament right now calling for a do-over. One analysis calculated that only 133 MPs — out of 650 — have publicly backed a second referendum.
Campaigners hope the number would go up even more if May's deal is voted down in Parliament.
But implementation would take time. The Constitution Unit research group at University College London estimates that it could take about five months to pull it off.
Britain is set to leave the EU in three. So it would need to negotiate an extension of the Brexit deadline with Brussels.
There is also the fraught issue of what would be on the ballot. Would it be a binary choice — a yes or a no? And if so, what would those choices be? May's Brexit deal versus a no-deal Brexit? Or May's deal versus remain in the EU? Those questions would produce radically different results.
All of this would be highly contentious.
Boris Johnson, who quit as Foreign Secretary over Brexit, said: "It would be infamous and pathetic of MPs to go back to the people before the political class had even succeeded in delivering on the first referendum result. It would so shake trust in politicians that the Government would suffer massively, and deservedly, in the next general election".
Many opponents of a second referendum say it would not only be divisive, but undemocratic — that the establishment can't hold votes until it gets the answers that it wants. Others say a referendum is inherently democratic.
"May's suggestion that a #PeoplesVote would 'overturn the will of the British people' makes literally no sense," tweeted J.K. Rowling, the Harry Potter creator and an arch-remainer. "Who does she think would be voting? The Chinese?"
Caroline Lucas, a Green Party MP, said: "I think it's right that people have the opportunity to have a first say on the actual facts of the deal. Two years ago, people didn't have any information, really, about what kind of Brexit we would be talking about, and now we know that every single version of Brexit that is being offered are versions that will make the whole country poorer."
