But Mrs May's decision to delay the vote sparked a fresh wave of speculation at Westminster about new letters of no confidence being submitted by Conservative MPs to the chair of the backbench 1922 Committee, Sir Graham Brady.
A majority of Tory MPs have publicly said they will back the PM in the vote, which runs for two hours from 18:00 GMT (7am NZT), but it is a secret ballot.
"I stand ready to finish the job", she said.
She also offered a sobering message about the challenges the government faces in getting its Brexit deal through parliament, with shifting groups of MPs advocating a series of incompatible options - from a second referendum to no deal.
Briefing EU lawmakers in Strasbourg, France, on this week's leader's summit, Juncker said Tuesday that "there is no room whatsoever for renegotiation" of the divorce deal.
She must now fly to Brussels on Thursday to appeal to her fellow European Union leaders to offer Britain what she told MPs must be a "legally binding" commitment that the Irish backstop will be temporary.
If she loses the vote of party legislators, taking place on Wednesday evening, May must step down. But the prime minister has said that she'll go - though not just yet.
Following the result, May said she was pleased to have received the backing of her colleagues, but she acknowledged that a significant number of them voted against her.
Ms Hewn said markets are "most concerned" with the prospect of a no deal Brexit.
Parliament has until January 21 to vote on the deal, a little more than two months before Britain's March 29 departure date.
United Kingdom government publishes full Brexit legal advice
Both May and the bloc insist the withdrawal agreement can't be changed, and rejecting it means leaving without a Brexit deal . However, the Government has ruled out making a plea to Brussels to renegotiate the withdrawal agreement .
With less than four months left until the United Kingdom is due to leave the European Union on March 29, May's Brexit deal is floundering, opening up prospects that run the gamut from a disorderly no-deal divorce to calling Brexit off.
A British Conservative Party official says Prime Minister Theresa May will face a no-confidence vote from party lawmakers.
Solicitor-General Robert Buckland said May told lawmakers at a meeting that "it is not her intention to lead the party in the 2022 general election".
The party membership would vote via a postal ballot on which of the two candidates should be party leader. "I am absolutely sure the prime minister will win", said Michael Gove, the most senior Brexiteer in May's government.
Speaking to BBC News, Ms Hewin said: "When the rumours emerged that there was going to be a leadership challenge or a confidence vote in the Prime Minister, we saw the pound falling quite dramatically last night".
May cancelled a trip to Dublin on Wednesday for talks with Irish Prime Minister Leo Varadkar amid the leadership challenge.
"The deal that we have achieved is the best deal possible, it is the only deal possible", he reiterated.
Earlier in the day, Mr Juncker told the European Parliament that there was "no room whatsoever for renegotiation" of the Withdrawal Agreement reached between the EU and United Kingdom last month.
Prospective leadership contenders are former foreign secretary Boris Johnson, former Brexit secretary Dominic Raab, home secretary Sajid Javid, and global development secretary Penny Mordaunt.
Parliament was supposed to approve a plan painstakingly worked out by Prime Minister Theresa May and the European Union for Britain's orderly departure from the 28-nation bloc.