But she also said any new Brexit plan must "deliver on the referendum result", which May has long interpreted to mean ending the free movement of workers to Britain from the EU and leaving the EU's single market and customs union.
Meanwhile, British lawmakers from all parties are trying to wrest control of the Brexit process from a Conservative government seen as a lame duck so that lawmakers can take over planning for Britain's departure from the EU.
And he is leading a plot for MPs to seize control of the negotiations if Mrs May can not get a Plan B backed by Parliament in the coming weeks. On 15 January, Parliament roundly rejected May's deal with the European Union, which lays out the terms for an orderly withdrawal.
To find a defeat in the U.K.'s recent political history comparable to May's 230 vote drubbing, one has to look back to 1924, according to the British Institute for Government, which appraised records since 1918.
During the debate, Corbyn said there is "no majority for this government's Brexit deal and there is no majority either for a no-deal scenario", which he said would be a "catastrophe".
Owen Smith spoke after the prime minister offered to meet opposition leaders following the failure of Labour's no confidence vote.
Anand Menon, Professor of European Politics at King's College London, told AFP that the EU "will be thinking hard about whether it's worth offering concessions given the number of MPs the Prime Minister has to win over". "But tonight's vote tells us nothing about what it does support - nothing about how - or even if - it intends to honor the decision the British people took in a referendum Parliament chose to hold".
Mike Hawes, chief executive of the Society of Motor Manufacturers and Traders, said parliamentarians "hold the future of the British automotive industry - and the hundreds and thousands of jobs it supports - in their hands".
As Tuesday's debate kicked off, Speaker of the House of Commons John Bercow announced which amendments he had chosen for debate from more than a dozen submissions. This government can not govern and can not command the support of Parliament on the most important issue facing our country.
Germany's foreign minister says "the time for little games is now over" on Brexit because the clock is ticking to avert a hard rupture between the United Kingdom and the European Union.
Turkey's Erdogan Announces Creation of Safe Zone in Syria Suggested by Trump
Erdogan's spokesman Ibrahim Kalin said Ankara would "continue to fight against them all", referring to IS and the YPG. Why does the U.S. want a safe zone? U.S. officials have refused to announce a timetable for any troop withdrawal .
Annegret Kramp-Karrenbauer, leader of Chancellor Angela Merkel's centre-right CDU party and her likely successor.
But there was little doubt in Westminster that Mrs May would hang on - and was likely to survive a motion of no-confidence tabled by Labour leader Jeremy Corbyn.
Tuesday's result isn't much of a surprise, coming five weeks after May had to postpone the original scheduled vote to shore up support for her deal.
May's political allies from Northern Ireland, the Democratic Unionist Party, also objected because the backstop treated Northern Ireland differently from other parts of the U.K. The party said that frayed the bond between Northern Ireland and the rest of the country. "But people are skeptical that she's going to get anything that's going to win over members even of her own party".
But with the Conservatives obliged to come up with a Brexit "Plan B", the pound could yet be in for a rough ride. Many members have been waiting months for the chance to vote on Brexit. And the bloc's highest court has ruled that it is OK for the U.K.to unilaterally reverse its decision to leave. It would basically be saying, 'We can't work this out.
"Please, please, tell us finally what you want to achieve", Weber said. "That is an extraordinary thing for a democracy to do". "The risk of a disorderly exit has increased with this vote and, while we do not want this to happen, we will be prepared for it". "A new plan is needed immediately".
An EU commission spokesman reiterated on Wednesday that the withdrawal agreement is not open for renegotiation.
On Monday, May and her counterparts in the European Union sought to assuage some of these concerns.
EU Council president Donald Tusk, who added the remaining EU27 "will remain united". Assurances from European Union leaders that the backstop is intended as a temporary measure of last resort failed to win over many British lawmakers.