As evidence for the claim that MPs might block Brexit, Barclay cited a parliamentary vote last week that will push the Government to come up with a Plan B within three working days if May's deal fails.
European Union leaders are preparing to delay Brexit until July or possibly longer if Parliament can not agree a deal, it has been claimed.
Liberal Democrat Brexit spokesman Tom Brake said: "Chris Grayling has lost the plot".
In a warning to Conservative rebels ahead of the vote, Brexit Secretary Stephen Barclay said that Brexiteers seeking "ideological purity" are in danger of seeing Britain not leave the European Union at all.
Lawmakers in the United Kingdom are set to vote Tuesday on May's Brexit plan after she shelved plans for a December vote when it became clear she would lose that vote.
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.
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".
He told Marr: "Clearly if Theresa May's deal is voted down, clearly if a general election takes place and a Labour government comes in - an election would take place February, March time - clearly there's only a few weeks between that and the leave date, there would have to be time for those negotiations".
Democrats Deliver Response to Trump's Prime Time Address
Leadership from both parties will join the president for their third meeting in the Situation Room later this afternoon. But Tuesday morning, Pelosi and Schumer announced that they would "deliver a response to President Trump's 9:00 p.m.
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 has also 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.
Danielle Haralambous, a United Kingdom analyst at the EIU, said: "Time is simply running out, and we're at a stage where Brexit can probably only happen in late March now in the unlikely event that parliament approves Mrs May's deal on 15 January, or if parliament supports leaving without a deal".
But he has insisted the United Kingdom should not afraid of a no-deal Brexit, despite forecasts from the Treasury and Bank of England warning that it could trigger an economic crisis worse than the 2008 financial crash.
Former minister Jim Fitzpatrick told the Commons on Friday that he was "not far away" from backing May's deal, saying the "danger of no deal is still there" and the PM's plan was "the only real alternative on the table".
"The prime minister herself has said this is not the flawless deal".
Mr Russell also said that the views of the people of Scotland, the Scottish Parliament and Scottish Government should not be ignored.