Members of Parliament (MPs) in the UK's lower chamber House of Commons voted 308 to 297 on Wednesday to back a motion demanding the government puts forward a revised plan within three days should May lose the vote on January 15.
The Commons amendment, tabled by Labour's Yvette Cooper, is created to limit the Treasury's ability to spend money on no-deal preparations, without the explicit consent of Parliament.
On the first of five days of debate on the deal, former global development secretary Andrew Mitchell said: "I've been astonished that she would bring back to the Commons a deal she knows she has absolutely no chance whatsoever to get through, and also with apparently no plan B".
Sir Keir also attacked the prime minister for now pushing ahead with the vote on her Brexit deal when "nothing has changed" to the terms of her agreement with Brussels.
Ms. May has already delayed the vote once, hoping to win more concessions from the European Union that would make her agreement more palatable to Tory rebels.
A previous amendment by Grieve, voted through by the Commons before Christmas, means any statement that follows a defeat is in itself amendable - thus allowing MPs to put forward their own alternatives for the future of the Brexit process.
"He is not impartial on this or frankly any other issue".
The amendment was tabled by Labour MP Yvette Cooper and former Tory cabinet minister Nicky Morgan in an effort to demonstrate the strength of opposition to no deal.
"It seems clear that May will lose the vote, the only real question is how much does she lose by", Usherwood added.
Tory MP Ken Clarke, who backed the amendment, said that those who did not like the amendment should "don a yellow jacket and go outside" to join some of the hard-right protesters who had harassed MPs outside parliament.
Under the EU's backstop proposal, Northern Ireland would have stayed in the single market and customs union while the rest of the United Kingdom withdraws, while Mrs May wanted Northern Ireland treated the same as the rest of the UK. Several business leaders have expressed concern about a "no-deal Brexit", saying it could cause economic chaos, and many companies have been stocking up on supplies.
Jeremy Corbyn urged Theresa May to now rule out a no-deal "once and for all".
Manfred Weber, a German conservative who heads the biggest group in the European Parliament, said in Berlin that "our colleagues in Britain's lower house carry great responsibility now - the agreement is on the table". Others have proposed a referendum asking voters if they prefer Ms.
"We are talking about 79 days until potentially crashing out of Europe without a deal - should our focus not be on the detail and the arguments about the process in this place, but getting on with a plan B if Parliament decides the government's plan is not the one for the people?"
But there is no clear majority for any single alternate course. That could yet play into Ms.
Speaking to MPs earlier, May said: "The only way to avoid no deal is to vote for the deal".
But she has little room to manoeuvre.
She pulled a scheduled parliamentary vote on the brokered withdrawal agreement last month, admitting it lacked the required support. The DUP has come out against Ms. The proposals would give Northern Ireland a veto over introducing any new areas of law and policy if the so-called Irish backstop provision in the Brexit deal is triggered. The Tories are also deeply divided.
But, combined with a vote late on Tuesday when the government lost on the finance bill, the defeats underline May's precarious position in parliament.