Labour leader Jeremy Corbyn said Labour would be voting against it because it "risk people's living standards", jobs and the NHS. "That's why Members of Parliament must reject this deal tomorrow".
In a later exchange, with the Conservative pro-Brexit MP Peter Bone, May expressed her scepticism about the so-called Malthouse compromise, outlined in an amendment to Wednesday's motion, which calls for the United Kingdom to leave the European Union without a withdrawal agreement, but with a form of transition period to lessen the impact of no deal.
"It's time that we have a general election and the people can choose who their government should be", Corbyn said on Tuesday after May suffered a humiliating 391 to 242 defeat when her Brexit deal was rejected by Parliament for a second time.
In his concluding remarks, he said: "The Prime Minister's deal has failed, she no longer has the ability to lead, this is a rudderless Government in the face of a huge national crisis".
But Tory former minister Nick Boles said this would amount to a no-deal exit and the European Union would not agree to it.
A cross-party amendment selected for consideration aims to "enable the House of Commons to find a way forward that can command majority support" on March 20, which could also start the process for "indicative votes".
The Work and Pensions Secretary said a no-deal Brexit would "do generational damage to our economy and security".
Dr Wollaston added on her second referendum proposal: 'For young people in this country, they face being wheeled into the operating theatre for major constitutional, social and economic surgery based on a consent form that was signed by their grandparents almost three years ago'.
But dismissing calls from Tory MPs to embrace a no-deal exit now, Mrs May said her deal remained the best way to honour the 2016 referendum result. "That's why MPs must reject this deal today", the politician noted. She won the vote by 412 to 202.
Some of her colleagues around the Cabinet table think it shows she has to tack to a closer deal with the EU.
Other ministers believe genuinely, still with around two weeks to go, and an European Union summit next week, there is still time to try to manoeuvre her deal through - somehow.
Amid reports Brexiteer ministers have been granted a free vote on this proposal, Tory MP Steve Baker told BBC News the plan - which would see Brexit delayed until 22 May - was "eminently reasonable".
She said: "I'm grateful... for the spirit in which they have sought to broker compromise in this House".
"If you're in the Government, then you vote the Government's position".