The PM has also faced further opposition to her deal from former Brexit secretary Dominic Raab, who used an article in the Sunday Telegraph to urge MPs to vote down Mrs May's "bad" deal and send a message to Brussels that the United Kingdom "will not be bullied".
People have to think long and hard about how they are going to vote.
Meanwhile Mrs May warned of a "catastrophic and unforgivable breach of trust" in democracy if Brexit is stopped.
Corbyn said Labour would vote against May's deal, and if she lost would start moves to trigger a general election.
This is too important for political game-playing and I urge Conservative MPs who back Brexit and others to back the deal.
Warning that there may be no consensus in the Commons around any possible outcome, the foreign secretary told Today: "If this deal is rejected, ultimately what we may end up with is not a different type of Brexit but Brexit paralysis".
Sir Vince said this could happen by cancelling Article 50 - which he noted would be "resented by lots of people" - or via a second referendum.More news: Everton enter the race for Chelsea outcast Batshuayi
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If a confidence vote failed, he'd be under pressure to back a second Brexit referendum, risking a backlash from the many Labour supporters who voted to leave the EU.
One of her predecessors, Sir John Major, called for Article 50 to be revoked as he warned it would be "morally reprehensible" to crash out without a deal.
- It emerged that 14 military planners have been deployed to four key Whitehall departments to assist with no-deal planning, according to a Freedom of Information request by the Observer.
He said if it is defeated, Britain should continue to press the European Union for a deal that "respects the referendum but if Brussels" "intransigence persists" we must be willing to leave the European Union at the end of March on World Trade Organisation terms'.
Transport Secretary Chris Grayling insisted the Government has put forward a "sensible compromise deal" before denying troops were being sought to help with no-deal Brexit traffic plans.
Mrs May was boosted on Thursday by two Tory backbenchers - her former policy adviser George Freeman, and Trudy Harrison - indicating they will back her deal, as well as by a call from Japanese PM Shinzo Abe for the United Kingdom to avoid no-deal.
Fitzpatrick, whose London constituency strongly backed remain, said "time is running out" and a so-called "people's vote" on the deal was "code for reversing original decision".
But former Brexit Secretary Mr Davis said the amendment also allows Britain to "go back to the European Union with our best and final offer".