LONDON — When the world last focused full attention on Prime Minister Theresa May of Britain, she had returned from a “begging tour” in Europe with a Brexit extension she had hoped never to ask for and was fighting for her political life with her Conservative Party in open revolt.
She won the extension, to Oct. 31, but she is still fighting for her political life, this time against the embarrassing backdrop of a rising Brexit Party helmed by Nigel Farage that is easily outperforming Conservatives in most opinion polls.
All that seems to have led Mrs. May to take a last, desperate gamble, by holding a fourth — and, almost certainly, final — vote on a plan to leave the European Union that Parliament has rejected three times already. The vote seems set for the week beginning June 3, which is also when President Trump is scheduled to make a state visit to Britain.
Mrs. May has promised to stand aside if Parliament approves her plan, but she could face the exit gate anyway if Parliament were to reject it a fourth time.
“Whatever happens next on Brexit, Theresa May’s departure from Downing Street is only a matter of time,” Mujtaba Rahman wrote in an analysis for the Eurasia Group consultancy, where he is the managing director for Europe. “Within a few months, therefore, the 120,000 members of the Conservative Party (just 0.26 percent of the electorate) will choose their next leader and the U.K.’s next prime minister.”
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The timing of the new vote is curious, landing as it does amid of the pomp of the Trump state visit and in the same week that the United States and Britain commemorate the 75th anniversary of the D-Day landings that presaged the end of World War II.
Already, the omens look bad, given the familiar array of opponents in Parliament to Mrs. May’s Brexit plan, which would keep Britain closely tied to the European Union at least until the end of 2020, and then extract it from the bloc’s main economic structures.
For weeks, government-initiated talks with the opposition Labour Party to find a bipartisan approach have plodded along without making noticeable progress. They are now considered to be on life support, though neither side wants to risk aggravating deeply threatening splits in the ranks by making big compromises or being blamed for pulling the plug on negotiations.
In truth, Mrs. May had little choice but to roll the dice like this, because the walls are closing in on her. On Thursday, she is scheduled to meet an influential committee of senior Conservative lawmakers who are threatening to change the rules that protect her from a formal challenge until December. That would open the way to her imminent ouster.
Now, she has a plan to present to them that could win her a few more weeks.
The Conservative Party lost more than 1,300 seats in local elections this month. A worse performance is expected in the European Parliament elections on May 23, with the Brexit Party, running on a simple platform of completing Brexit promptly, even if that means leaving without a deal, is attracting many disenchanted Tories.
Mrs. May is wagering that big losses in the European elections can be turned to an advantage, because Labour is likely to suffer, too. The hope is that, with the looming prospect of a no-deal Brexit or no Brexit at all, Mrs. May can persuade enough Labour lawmakers from pro-Brexit areas to join loyal pro-Brexit Conservatives to get her plan approved.
In another tactical move, Mrs. May is promising to bring to Parliament not a repeat of her thrice-defeated plan, but a specific piece of legislation, that she hopes might be more attractive to opposition lawmakers.
But the odds do not look good unless Labour can be fully won over. That is because of the resolute opposition from hard-line, pro-Brexit Conservative lawmakers to the “backstop” provisions in her agreement. The provision would avoid a physical border between Northern Ireland and the Republic of Ireland, but it could also keep Britain tied to some European rules indefinitely — defeating the purpose of Brexit, in the hard-liners’ view.
One Conservative lawmaker, Owen Paterson, told the BBC that his faction, known as the European Research Group, would vote against. The group of 10 lawmakers from the Democratic Unionist Party of Northern Ireland, who normally support the government, have also pledged to oppose the plan.
“The question will be, ‘What has changed?’” Nigel Dodds, the leader of the D.U.P. caucus in Parliament, said in a statement. “Unless she can demonstrate something new that addresses the problem of the backstop, then it is highly likely her deal will go down to defeat once again.”
For her part, Mrs. May argues that, any potential successor would inherit the same problem: The math in Parliament will not change. The only way to alter it would be a general election, and, given voters’ current anger, few Conservatives want such a contest right now.
But it looks as if the stasis over Brexit has left the Conservative Party in such a funk that it believes that another leader could not do any worse.
Labour leaders seem unlikely to offer a lifeline. Mrs. May still hopes to lure them with an offer to keep Britain in a type of customs union with the bloc — eliminating the need for tariffs and for many border checks on goods — until the next general election.
But Labour officials dismiss that as insufficient, pointing out that any agreement could be torn up by her successor, particularly a hard-line Brexit supporter. They are also aware that a large faction of their party wants a second referendum on any deal, meaning that any agreement with the Conservatives would threaten party unity.