"We want to see that deal go through on March 13, but we need the insurance that if it doesn't get through the default is no longer to allow this country to leave without a deal but to extend Article 50", she said.
May said that, if that fails also, the government would put forward a motion "on whether Parliament wants to seek a short limited extension to Article 50" - referring to the trigger mechanism by which Britain would leave the European Union.
The EU has said it will consider an extension to the Brexit process, but only if Britain can offer evidence that such a delay would break the deadlock in parliament.
The Caroline Spelman/Jack Dromey amendment - The two MPs say it could "pave the way" for legislation to force the government to provide an opportunity to extend Article 50.
The move is likely to avert a serious ministerial rebellion.
Corbyn will also seek to enshrine his party's "five Brexit demands" in law by tabling a further amendment to the government's Brexit motion.
British newspapers reported this week that May faced a number of cabinet resignations if she had not given MPs a vote to delay Brexit.
The coalition was awaiting further reassurances from ministers on Wednesday, including from the Brexit secretary, Steve Barclay.
Ms Thornberry said: "I've seen some nonsense that I "misspoke" earlier on a public vote".
And May has repeatedly said that the no-deal threat must be kept on the table in order to wrest concessions from Brussels needed to push her deal through parliament.More news: Stranded Amtrak train with 183 passengers is finally moving again
Cabinet sources suggested any decision on whipping MPs to vote a certain way would only be made once the meaningful vote had been lost.
"We've had a tick-up in the pound but the market has front-run these developments before, only to be disappointed", said Kallum Pickering, UK economist at Berenberg.
Corbyn said on Tuesday that May's deal must also face "a confirmatory public vote" if it is ever approved.
An exit deal negotiated by Prime Minister Theresa May was rejected by an overwhelming 230-vote margin last month.
The prospect of Britain suffering an economic shock next month eased Tuesday after the British government paved the way for a delay in the country's departure day.
"Given the controversy about how Cooper-Letwin are planning on passing that bill, to suspend parliamentary rules for a period of time, I think that some of her backbenchers who might have been rebelling against the government tomorrow might end up backing the PM", Maddy Thimont Jack, a researcher at the Institute for Government in London, told Al Jazeera.
Driving the point home, May said the vote would mean that "the United Kingdom will only leave without a deal on the 29th of March if there is explicit consent in the House for that outcome" - a responsibility-sharing statement that elicited grumblings and cross-talk in the chamber. "But ultimately we felt like we had been left with no other option". I can not, and will not, accept that on behalf of the people of Portsmouth. "But that causes its own party problems too".
Bank of England Governor Mark Carney has warned that the Brexit uncertainty that has dogged the British economy over the past couple of years will remain even if lawmakers agree to a withdrawal agreement with the European Union in coming weeks. "You can probably only pull that cord once", a Whitehall source said.
May said she and her team - Secretary of State for Exiting the European Union Stephen Barclay and U.K. Attorney General Geoffrey Cox - have been in "focus discussions with the EU to find a way forward that will work for both sides, and we are making good progress in that work".