A number of Conservative backbenchers also attempted to hold an unofficial vote of no confidence in their party leader on Wednesday, but were blocked by party authorities.
At its summit meeting in late March, the European Union made a decision to postpone the date for Brexit from March 29 to April 12 unless Britain's House of Commons can pass the draft deal. Pro-EU legislators argue it is worse compared to the U.K.'s current status as a EU member.
Tadcaster MP Nigel Adams has quit as a junior minister this morning in protest over Theresa May's latest Brexit policy.
"We have agreed a programme of work to ensure we deliver for the British people, protecting jobs and security".
And Chancellor Philip Hammond fuelled speculation that the Government may be preparing to accept a public vote as part of the price for securing a deal that can get through the House of Commons, describing a referendum a "perfectly credible proposal" in a interview on ITV1's Peston.
Her plan is to seek acceptance for the legally binding arrangement - which puts out in detail the conditions of Britain's departure from the European Union - following securing cross-party political support to get a vision of future ties between the United Kingdom along with the bloc.
But European Commission President Jean-Claude Juncker said in Brussels that Britain would not get any further short delays unless its parliament ratified a deal by April 12 - the date set by EU leaders as the effective cut-off for avoiding the European Parliament elections.
The bill, put forward by Labour Party's Yvette Cooper, now needs to be approved by the House of Lords before it becomes law.
Corbyn has welcomed the talks, but the invitation poses a threat for his divided Labour Party - some members and lawmakers are demanding a second referendum on any deal while others fear being blamed for helping pass May's much-criticised agreement.
Within minutes of May reading her statement, Jeremy Corbyn offered a tentative response to May's announcement.
Mr Boris Johnson, the face of the 2016 Brexit campaign, said a compromise with Labour would betray the referendum, asserting that the world's fifth biggest economy could be outside the European Union but still subject to European Union rules.
"It is clear we will now end up in the customs union".
In a marathon session of Prime Minister's Questions, May was buffeted by hostile interventions from her own MPs.
Rank-and-file Tory Bill Cash called the bill an "utter rubbish dump", while his Conservative colleague Mark Francois complained it had been "rammed" through the Commons "in barely four hours".
Brexit Secretary Stephen Barclay said failure by May and Corbyn to reach a compromise would prompt the two sides to try to come up with mutually-acceptable options that would be put up for binding parliamentary votes.
"The PM's head of communications Robbie Gibb is a hard Brexiter who wants to destroy the PM's new search for a cross party compromise", he wrote on Twitter.
Going back to what happens next...
"Crucially, the government stands ready to abide by the decision of the House".
Parliament narrowly rejected a proposition for a referendum Last week. Leaders of the bloc, exasperated by the chaos in London, say they will only grant a delay to Brexit if Britain comes up with a workable new plan.
There were signs of divisions in Labour, too. But until now Mr Corbyn has said that he is strongly opposed to the nature of the backstop.
May dramatically ended her courtship of her own party's holdouts and resistant Northern Irish allies by turning to the main opposition Labour Party this week.
He added that he had also raised the topic of a second referendum.