European leaders agreed to endorse the prime minister’s Brexit blueprint after just half an hour of talks at a special summit in Brussels on Sunday, which comes after 18 months of wrangling behind the scenes.
Ms May’s focus now shifts to the battle to get the deal through parliament amid opposition from all sides, with more than 90 Tory MPs publicly expressing disapproval of the plan.
It comes as European leaders warned the UK would not be offered a better deal if Ms May’s blueprint is overturned in parliament.
Mr Hunt appealed to his party to act in the “national interest” but admitted the prime minister faced an uphill battle to win over MPs before the crunch vote in parliament in December.
Asked how many Tory MPs would vote against the deal, the foreign secretary told the BBC’s The Andrew Marr Show: “That’s a very difficult question and the arithmetic at the moment is looking challenging but a lot can change over the next two weeks.
“I think what all my colleagues will be doing is thinking what is in the national interest.”
Asked if a defeat could mean Ms May’s government could collapse, he said: “It’s not possible to rule out anything.”
Mr Hunt also appeared to suggest that the deal could be a “staging post” towards a better agreement and said it “mitigates most of the negative impacts” of Brexit.
He said: “I think the truth is there are compromises in this deal, but my colleagues in the House of Commons will be looking at this and they will say that we have got between 70 and 80 per cent of what we want and the question is, can this be a staging post to getting 100 per cent of what we want?”
However, DUP leader Arlene Foster threatened to bring down the government over the deal, making clear there were no circumstances under which her party would back it in the Commons.
And she warned that Ms May could not count on the support of the DUP if a parliamentary defeat triggered a vote of no confidence in the prime minister.
She insisted the DUP’s confidence and supply agreement – where her 10 MPs prop up the government - remained “live” but added: “If it came to the situation that parliament did decide – and there is no evidence that they are going to – if they did decide to back this deal then obviously we would have to review the confidence and supply agreement.”
“As far as I can see, in parliament, she does not have support for this deal,” Ms Foster said.
Ms Foster suggested the DUP could back a Norway-style deal allowing the UK to stay in the EU single market, as long as there was no separation of Great Britain from Northern Ireland.
Former Tory leader Iain Duncan-Smith said it would be “very, very difficult” to support the deal as he claimed “far too much has been given to the EU”.
He told Sky News’s Sophy Ridge on Sunday: “Well I don’t want to stay in the EU. I campaigned and voted to leave the EU.
“I don’t believe that, so far, this deal delivers on what the British people really voted for, take back control of your borders, your laws, your money. I think it has ceded too much control.”
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Labour MP Lisa Nandy, who represents Leave-backing Wigan, said it was “inconceivable” for her to back the deal, in a blow to the prime minister’s hopes of support from Labour ranks.
Ms Nandy called for an extension to Article 50 to head off a no-deal, adding: “There is a real prospect now of no deal because many of those Leave voters, contrary to the opinion in Westminster, actually dislike this deal more than the Remain voters who contact me on a regular basis.”
However European Commission president Jean-Claude Juncker fired off a warning to MPs seeking to derail the deal, saying: “This is the best deal possible for Britain, this is the best deal possible for Europe.
“This is the only deal possible.’’
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