LONDON — Fighting growing calls for her to stand aside quickly, Prime Minister Theresa May of Britain suffered a significant blow Wednesday when a Cabinet colleague resigned, saying she could no longer support the government’s latest plan for leaving the European Union.

The Cabinet member, Andrea Leadsom, left her position as leader of the House of Commons at the end of a day of swirling rumors about a Cabinet coup against May. There is a ferocious backlash among Conservative lawmakers against her latest plan to resolve the Brexit crisis.

In her resignation letter, Leadsom said she was leaving because she no longer believed that the government’s approach would deliver on the 2016 referendum decision to leave the European Union.

She could not, she said, announce planned new legislation “with new elements that I fundamentally oppose.”

That was a reference to a promise made by May on Tuesday that under her revamped Brexit proposal, lawmakers would be able to vote on whether to hold a second referendum. Lawmakers would also decide whether their country should continue to follow — at least temporarily — the EU’s customs rule book.

In response to Leadsom’s letter, May’s office at 10 Downing Street said it was “disappointed that she has chosen to resign, and the prime minister remains focused on delivering the Brexit people voted for.”

Leadsom, a hard-line Brexit supporter, contested the Conservative leadership in 2016 and made the final shortlist of two, but ultimately withdrew, leaving May the sole candidate.

By her own admission, May’s turbulent time in Downing Street is now entering its final stages, and Leadsom is likely to be a candidate again when the contest to succeed her formally starts.

With May’s leadership already on life support, her latest Brexit proposal, announced Tuesday, was seen as her last chance to salvage some sort of legacy from her time in power by persuading Parliament to accept a variant on a blueprint it has already rejected three times.

The Conservative Party is now confronting a quandary: Should they allow their wounded pilot to go down in flames or should they press the ejector button first?

So negative was the reaction to her proposal that some lawmakers believe that putting it up for a vote would make matters worse, not better, because another crushing defeat would complicate life for her successor. Nigel Evans, a member of an influential committee of Conservative lawmakers, said that May should “make way for fresh leadership without handcuffing her successor to a poisoned baton.”

Throughout Wednesday, pressure mounted on May to scrap the vote that she is still promising for the week beginning June 3, and to name the date of her departure immediately.

May’s ability to dig deep and survive any amount of political pain has been perhaps the defining feature of her period in power. On Wednesday, she defended her Brexit blueprint doggedly in Parliament as she has done so often before, even as she conceded that “in time another prime minister will be standing at this dispatch box.”

But the support a prime minister would normally expect was conspicuously absent, with many of May’s fellow Conservatives staying away from the chamber and leaving her to fend for herself. All the while around Parliament, an expanding crowd of hopefuls are lobbying Conservative lawmakers for support in the looming contest for her job.

In one last desperate act, May has revamped a proposal that would keep Britain tied to Europe’s main economic structures at least until the end of 2020, then take it out of the bloc’s customs and trading system.

But constructing a revised deal that might gain the support of a wider coalition of lawmakers, including some from the opposition Labour Party, has put May on a political tightrope.

With her revamped plan, May aimed to win over Labour lawmakers by offering the opportunity to vote on whether to put any plan for Brexit to a second referendum. Lawmakers would also be allowed to vote on whether to keep Britain, temporarily, in a type of customs union with the EU that would eliminate tariffs and many checks on goods at borders.

But while the Labour leadership rejected the concessions as insufficient, many of May’s pro-Brexit lawmakers were horrified, and several of those who had reluctantly supported the government in its last Brexit vote have said they would not do so again.

Another defeat would be particularly problematic since May is not offering lawmakers a general vote on her deal but one on specific legislation to take Britain out of the bloc. Losing that would limit the options for a new prime minister, who would not be able to bring back the bill in the same parliamentary session.

On Wednesday, one Conservative lawmaker, Nicky Morgan, appealed to May to reflect on whether to proceed with her Brexit vote, noting that the “consequences of it not being passed are very serious.”

Earlier, the environment secretary, Michael Gove, gave an agile and evasive interview to the BBC in which he hinted that the bill might not come forward as planned — without saying whether it would.

That question is connected to the timing of May’s departure.

Earlier this year she promised to step down if lawmakers voted for her deal. Then, last week, she told senior Conservative lawmakers that, if her proposal was rejected again, she would set out a timetable for her successor to be chosen.

Convincing her to withdraw the proposal would be an effective admission that she cannot win, and would seem to fulfill that condition — giving lawmakers a way to send her packing without shouldering direct responsibility.

Though May now has only threadbare support — at best — from her Cabinet, senior colleagues are divided into factions depending on their willingness to contemplate the huge economic risks of withdrawing from the EU unilaterally. With little trust among them, Cabinet ministers have struggled to maneuver against May, and leveraging her out of Downing Street quickly is also complicated by the upcoming political calendar.

Late on Sunday, results will start coming in from European elections, in which opinion polls suggest the Conservatives will be humiliated. That would put May under pressure to resign immediately. But Monday is a public holiday, and Parliament will be on vacation until June 4, when President Donald Trump is scheduled to be in Britain on his state visit.

If she can survive this week, May is likely to be able to continue until after the visit. But sooner or later, the time will come for her to lay down a timetable for the election of the next leader of the Conservative Party.

This article originally appeared in The New York Times.