Shadow chancellor John McDonnell claimed Labour had won a "victory in forcing the Prime Minister to set a date for the meaningful vote", but clarified: "Jeremy has taken the sense of the House of Commons which is clearly demanding a vote this week".
Mr Corbyn tabled a motion on Monday night, calling on MPs to declare they have no confidence in the prime minister because she failed to have a vote on her Brexit deal straight away.
The leader of the opposition Labour Party sought to turn up the pressure by lodging a motion of no confidence in May for not quickly re-scheduling the vote by lawmakers on her Brexit plan that she delayed last week.
Speaking in the Commons on Monday afternoon, May announced the do-or-die date for her European Union withdrawal agreement, having cancelled vote last week in the face of a huge defeat by her own party.
But she said that, with the fate of her deal in the balance, the Government had a duty to step up preparations for the possibility of a no-deal Brexit.
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To a look of bewilderment from Theresa May, Greening said that the prime minister was "not allowing debate".
A government source said Downing Street would not allow time in parliament for "a stunt" and if Labour was serious it should attempt a full vote of no confidence in the government, which would bring it down if backed by parliament.
It's very clear that it's bad, unacceptable that we should be waiting nearly a month before we have a meaningful vote on the crucial issue facing the future of this country.
Business Secretary Greg Clark told BBC radio that "parliament should be invited to say what it would agree with" instead of just criticising May's deal.
In the face of calls for a second referendum to resolve the impasse, May has argued that this would betray the 2016 result and undermine public confidence in politics.
Nevertheless, it remains official Labour policy to try and force a general.
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She insisted she "faithfully and firmly reflected the concerns of this House over the Northern Ireland backstop" and claimed the European Union had committed that the controversial provision in the Brexit deal could be avoided and would only be temporary.
In protest, in the last hour, he put down a motion of no confidence in the Prime Minister as an individual, but it is unclear when that vote might be held and how it might threaten the survival of the government.
"He also called on her to hold the vote sooner".
"I lost the vote last week - and if you lose, that is ultimately conclusive", he told Sky News.
"Let us not break faith with the British people by trying to stage another referendum", she told parliament on Monday. However, it may well be easier to win than a vote of no-confidence in the government.
The announcement was met with anger by many MPs, who believe pushing the vote into the new year will leave them with the choice of May's plan or no deal.
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