– Not long ago, staging a second Brexit referendum was a fringe idea — a pipe dream of a handful of “remoaners” who had voted to remain in the European Union, cheered on by unpopular figures from yesteryear.

But the once barely imaginable is now becoming remotely possible.

The British may be headed toward one of history’s greatest do-overs — another vote to ask if they really, really want to leave the E.U., after all they know now about breaking up being hard to do.

Prime Minister Theresa May has repeatedly ruled out a second referendum, arguing that the people already voted, in June 2016, when Brexit won 52 percent to 48 percent. Now, she says, the job is to deliver on that result.

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 E.U. and May’s Cabinet has little chance of passing Parliament, more and more Brits 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 Brits 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 in the E.U.

But 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 a trade deal with the E.U. like the one Norway has, 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 current 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 lawmaker and remainer, told the BBC.

Pro-Europeans were thrilled last month when the Conservative lawmaker and remainer Jo 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,” Johnson wrote in his resignation letter.