The beleaguered premier is in the last throes of a tumultuous rule focused all-but exclusively on guiding her fractured country out of the European Union.
But three overwhelming rejections by parliament of the terms she struck with the other 27 nations last year have forced Britain to miss the original March 29 departure date and plead for more time.
Anxious members of May's party met behind closed doors Wednesday to discuss changes to the rules that would let them vote no-confidence in her leadership in the days to come.
Her woes were made worse when Andrea Leadsom -- one of cabinet's strongest Brexit backers -- resigned from her post as the government's representative in parliament over May's handling of the slowly-unfolding crisis.
"I no longer believe that our approach will deliver on the (2016) referendum results," Leadsom said in her resignation letter.
In her response May thanked Leadsom for her "passion, drive and sincerity", but took issue with her assessment of the government's Brexit strategy.
"I do not agree with you that the deal which we have negotiated with the European Union means that the United Kingdom will not become a sovereign country," May said.
May is now paying the price for failing to deliver on the wishes of voters who chose by a narrow margin in 2016 to break their uneasy four-decade involvement in the European integration project.
Her Conservatives are set to get thumped in European Parliament elections Thursday in which the brand new Brexit Party of anti-EU populist Nigel Farage is running away with the polls.
May has already promised to step down no matter the outcome of her fourth attempt to ram her version of Brexit through parliament in early June.
But even that sacrifice -- and a package of sweeteners unveiled Wednesday that included a chance for lawmakers to get a second Brexit referendum -- failed to win hearts and minds.
"It's time for the prime minister to go," Ian Blackford of the pro-EU Scottish National Party told May as she tried to defend her latest proposals in parliament.
"Will she do it?"
May ignored the question and called the upcoming vote Britain's last chance to leave the EU with a negotiated deal that can avert economic chaos.
Parliament should "stop ducking the issues and get on with the job that British people instructed us to do," she said.
Many of Thursday's newspaper front pages pictured May apparently with tears in her eyes. "May set to go after Brexit fiasco," said The Sun tabloid.
Things look set to get even worse for May in the days and weeks to come.
The European elections are being interpreted in Britain as a referendum on Brexit and on May's ability to get the job done. They make grim reading for the government team.
A YouGov survey Wednesday showed Farage's Brexit Party claiming 37-per cent support.
The pro-EU Liberal Democrats were second on 19 percent. The main opposition Labour Party was on 13 per cent and May's Conservatives were lagging in fifth place with just seven per cent.
"If we win these elections and win them well, we have a democratic mandate," Farage said Thursday.
Liberal Democrat leader Vince Cable told supporters that a vote for his party was "a vote to stop Brexit".
His group's open rejection of Brexit appears to be resonating with pro-EU voters who would normally back one of the two main parties.
May is still hoping to stay in power long enough to somehow win parliament's approval of the EU divorce terms before its summer recess begins on July 20.
This would let the country leave at the end of that month -- as long as lawmakers reject a second referendum.
Otherwise the process could be delayed until October 31 -- the deadline set by the EU -- or even later if its leaders grant Britain another postponement.
But pressure within both May's government and party is building for her to go now so that a new leader can rescue the process before Britain crashes out without a deal.
UK media reports said that Wednesday's meeting of Conservative parliamentarians discussed changes in rules focused on pushing May out the door within days.
The field of candidates to succeed May is led by former foreign secretary Boris Johnson -- a divisive figure who enjoys relatively strong public support.
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