Jean-Claude Juncker, European Commission president, said that despite Prime Minister Theresa May's struggles to get the deal through Parliament, he continues to hope she can secure backing for it in a vote on Tuesday.
In an interview with BBC Radio 4's Today programme, Mr Hunt warned that failure to deliver Brexit would be "incredibly damaging" for the United Kingdom and something the country would regret for "many, many generations". An overwhelming 66 per cent say she should carry on in No 10 if she loses on Tuesday, with only 26 per cent in favour of her stepping down.
"What is more likely if this deal is rejected is that we have the risk of Brexit paralysis and when that happens no one knows what might happen and the big risk, and what people worry about, is that we don't actually deliver what people voted for", Jeremy Hunt told Sky News.
With just two days to go before the Commons vote on her withdrawal agreement, the Prime Minister pleaded with parliamentarians to "do what is right for our country" and back her controversial exit plan.
They said a "sizeable number" of Labour MPs would vote against a second referendum "in any circumstance" while only a "really, really small number" Tories would back it. Some of you put your trust in the political process for the first time in decades.
A senior shadow cabinet member said: "There is now recognition that we can not wait any longer".
"Doing so would be a catastrophic and unforgivable breach of trust in our democracy".
The Sunday Times reported that rebel lawmakers were planning to wrest control of the legislative agenda away from May next week with a view to suspending or delaying Brexit, citing a senior government source.
BBC political correspondent Chris Mason said one possibility was that backbenchers could legally compel the government to delay Brexit beyond the set departure date - a proposal some MPs have already called for.
My best guess is that events are going to lead to Article 50 being postponed/extended, which in turn could mean that Brexit never happens.
Most British lawmakers also oppose the prospect of leaving the European Union without a deal.
On Monday the debate on the meaningful vote on Mrs May's deal will resume for a fourth day.
But the source said that the party is preparing to make daily decisions next week on whether to call a no confidence vote in the government if her deal is rejected by MPs. He pledges to back an amendment proposed by Labour MPs on the issue.
Last week the government was defeated twice in the Commons on Brexit votes.
While Grayling stopped short of predicting riots on the street if Brexit was weakened or reversed, he painted a picture of a "less tolerant society" and a "more nationalistic nation", as indicated by the incident with pro-Remain MP Anna Soubry.