It must approve the Withdrawal Agreement Bill in order to ratify Britain's exit from the bloc.
Brexit has been delayed until October 31 as MPs failed to reach an agreement on how best to exit the EU.
"I talked to colleagues and some who voted for it last time now think it's dead and will vote against it this time".
They say the definition of insanity is doing the same thing over and over again and expecting a different result, but it seems to have been the prime strategy for May, the beleaguered Tory leader.
But the Brexit delays have caused huge anger among her Conservative MPs as well as voters, and the party is braced for an electoral drubbing at European polls next week.
Asked if she would resign if the bill was defeated, May told reporters she was sure Members of Parliament (MPs) would do not forget to respect the referendum result.
May opened talks with Labour six weeks ago, acknowledging that entrenched opposition from her own side meant she needed help from across the political divide to pass her Brexit deal.
The House of Commons has rejected May's divorce deal three times but has, as yet, been unable to agree on an alternative path.
Kim, Kanye welcome fourth child via surrogate
One contestant told Khloe: "After I was injured, I had to have several surgeries and spend some time in hospital. The couple has not yet shared the little one's name, but fans are excited to learn the moniker they choose.
An anti-Brexit protester is pictured outside the Houses of Parliament in London, Britain May 15, 2019.
While European Union elections have always been seen as a safe place for mid-term protest votes to take place by the political establishment in the United Kingdom, polling showing that the month-old Brexit Party is now beating the Conservatives in even general election polling has sent shockwaves through Westminster.
Before her deal was defeated the last time, by 344 votes to 286 on March 29, May had promised to resign if it was passed.
This could keep Britain in a customs union with the EU after Brexit to avoid border checks that might jeopardise peace in Northern Ireland.
The DUP, on whose support May depends to command a majority in parliament, says efforts to avoid a "hard border" between Northern Ireland and the Republic of Ireland - keeping Northern Ireland largely aligned with the European Union until a new trade deal can be agreed, also known as the "backstop" position - undermines the integrity of the United Kingdom, creating a trade border between Northern Ireland and Great Britain.
Brexiteer and Conservative MP Steve Baker said bringing the bill forward "over the heads" of DUP MPs - on whom the government relies for a majority - would "eradicate the government's majority".
Prime Minister Theresa May was due to meet Jeremy Corbyn, leader of the opposition Labour Party, later on Tuesday to discuss the impasse in their cross-party Brexit talks, a Labour Party spokesman said.
"We have serious concerns about negotiating with a government that is in the process of disintegration and what has been said about what might happen if a new Tory (Conservative) leadership is in charge", a Labour spokesman said. It played down suggestions that the party was considering abstaining in the first vote on the Bill.