May faces a vote of no confidence on Wednesday evening sparked by MPs from the anti-EU wing of her Conservative party, plunging her into her biggest crisis since taking office after the 2016 Brexit vote.
Many of her cabinet ministers and other MPs were quick to support her, however, and pound rose amid reports that enough had already declared their backing for her to win.
In a defiant statement in Downing Street, May said she would contest the vote "with everything I've got".
She warned that her ouster would spark a leadership contest that would leave the terms of Britain's departure from the European Union for weeks, even as Brexit looms on March 29 next year.
"Weeks spent tearing ourselves apart will only create more divisions," May said, adding: "I stand ready to finish the job."
British PM delays Brexit deal vote but EU warns no renegotiation
Addressing the House of Commons later, she said a contest to replace her "would mean either delaying or stopping Brexit".
If May loses, her successor would be chosen from existing Conservative MPs and would automatically become prime minister.
But if she wins, she will be immune from further challenge for a year. The result is due around 9 pm (2100 GMT).
Brexit supporters have for months threatened to submit the 48 letters from MPs needed to trigger a confidence vote, in protest at her strategy to keep Britain close to the EU after leaving.
The last batch of letters came in after May — facing a heavy defeat — sparked fury among MPs by delayed a parliamentary vote scheduled for Tuesday on the Brexit deal she agreed with EU leaders last month.
Within minutes of the news being announced on Wednesday morning, a clutch of senior ministers rallied to May's support — including many who might succeed her.
"The last thing our country needs right now is a Conservative party leadership election," tweeted Home Secretary Sajid Javid, tipped as a future leader.
But prominent Brexit-backing MP Jacob Rees-Mogg said it was "time for Mrs May to resign".
May was informed of the challenge late on Tuesday, after returning from a tour of European capitals in an attempt to salvage her Brexit deal.
She had promised MPs when she delayed the vote that she would seek "assurances" about their concerns on a so-called "backstop" plan to keep open the border with Ireland after Brexit.
Theresa May's ministers trigger confidence vote plunging Brexit in chaos
Conservative MPs and May's Northern Irish allies, the Democratic Unionist Party (DUP), fear a plan for a temporary customs arrangement with the EU will become permanent.
May received sympathy from EU partners on her trip but firm rejections of any attempt to reopen the Brexit deal, which was only secured after 17 months of excruciating talks.
German Chancellor Angela Merkel said on Wednesday — the day after meeting May in Berlin — that she still "has hope for an orderly exit" but "no intention to change the exit agreement".
"We have little time, but we still have time," the German leader said.
May cancelled a trip to Dublin on Wednesday for talks with Irish Prime Minister Leo Varadkar, but is still expected to attend an EU summit in Brussels on Thursday and Friday.
May has said the parliamentary vote on Brexit will be held by January 21, but MPs fear it will be delayed again.
A furious opposition Labour leader Jeremy Corbyn accused May on Wednesday of being "contemptuous of parliament".
"There can be no more excuses, no more running away, put it before parliament and let's have the vote," he demanded.
University of Westminster policy professor Pippa Catterall it would be in May's interest to delay the vote on her Brexit deal until the process was "down to the wire... so in the end parliament is faced with the choice: my deal or no deal".
May could face a further no-confidence motion from opposition parties if she survives Wednesday's vote.
Labour has held off from attempting to topple May until it can be sure of succeeding.
A lot will hinge on DUP, which has propped up May's government for more than a year.
DUP leader Arlene Foster said on Wednesday she was not "surprised" by the no-confidence motion but focused on "the fact that the backstop needs to be taken out of that withdrawal agreement".
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