The prime minister has negotiated her own deal with the European Union but most British lawmakers hate it.
"I will contest that vote with everything I have got", she said, adding that removing her will not change anything.
Instead, she said she would visit European leaders and seek "additional reassurance" on some of the deal's more contentious elements.
She replied: "No, I have been here in Europe dealing with the issue I have promised Parliament I would be dealing with".
Had a majority voted against her, May would have been forced to resign as party leader and would have been expected to stand down as prime minister. A leadership election was sparked, but it never went to a vote after the rival candidate pulled out, leaving May as the only choice.
If she loses the confidence vote, May must step down and there will be a contest to choose a new Conservative leader.
Downing Street described talks with Mr Rutte as "constructive" and said the leaders agreed "to work together to find a way through", while in Berlin Mrs May and Mrs Merkel agreed to "keep in close touch on this in order to get the deal over the line".
The backstop is "the rule that either the Province [of Northern Ireland] or the whole of the United Kingdom must obey European Union rules until Brussels agrees that a hard border with Ireland is not a prospect", according to the Evening Standard.
Supporters of Brexit admit there may be some short-term pain for Britain's $2.9-trillion economy, but say it will prosper in the long term when cut free from the EU, which they cast as a failing German-dominated experiment in European integration.
If May wins, she remains in office and can not be challenged again for 12 months.
Pro-Brexit demonstrators wear tape accross their mouths and hold placards outside the Houses of Parliament in London.
"The deal we achieved is the best possible. As time is running out, we will also discuss our preparedness for a no-deal scenario".
"We are just at the start of the negotiations and the start of the discussions", she said after meeting with the EU Council's Tusk. But Sir Graham Brady, the chairman of the Conservatives in Parliament, admitted that, amid the chaos of Brexit, no time can be wasted, and that the Conservatives are "very keen the matter should be resolved as rapidly as possible". But at a closed meeting with Conservative lawmakers before they were due to decide her fate, she announced she would not take the party into the next election due in 2022, two lawmakers present told reporters. It comes days after May postponed a vote to approve the divorce deal to avoid all-but-certain defeat.
But her decision to cancel Tuesday's Parliamentary vote on her deal at the last minute proved to be the final straw for many who had previously given her the benefit of the doubt.
Former Environment Secretary Owen Paterson accused May of acting like a "supplicant" in dealings with the EU. Then it would fall to her successor to try to sort out Britain's Brexit mess.
Opposition lawmakers expressed astonishment and outrage at the Conservative civil war erupting in the middle of the fraught Brexit process.
May is set to face a vote of no-confidence in her leadership after the required 48 MPs from her Conservative Party filed letters with the influential 1922 Committee, which represents rank-and-file Conservative MPs in the House of Commons.
While EU officials ruled out renegotiating the divorce agreement, European Commission President Jean-Claude Juncker gave May a crumb to take back to lawmakers: "room enough" might exist for "clarifications and further interpretations" to be made at a leaders' summit Thursday, he said.
With this victory, May's leadership can not be challenged again for a year. European Union leaders tried to stay out of the fray.