Four days after the 2016 vote for Brexit, Jeremy Hunt called for a referendum on the withdrawal agreement. I remember it well because his Daily Telegraph piece appeared five hours after I proposed the same thing in The Independent. Hunt’s aides joked that they had borrowed my idea, but it was a coincidence.

As the new foreign secretary, Hunt now has the opportunity to revive his proposal. He won’t, of course. A Remainer turned “Re-Leaver”, he wants Conservative MPs and members to know he’s a fully paid-up Brexiteer because, along with about 20 rivals, he wants to succeed Theresa May.

Although several friends campaign tirelessly for a “people’s vote” on May’s withdrawal deal, I’ve never believed they had a chance of winning. Until this week, that is. Everything has changed, as May never says. The softer Brexit she forced through the cabinet at Chequers and yesterday’s white paper might provide the basis for negotiations with the EU which produce a deal later this year. May’s biggest challenge now is not Brussels but how on earth to get her agreement approved by the Commons.

The prime minister was not shaken (or that surprised) by the resignations of David Davis and Boris Johnson, and had wargamed such moves before the Chequers summit. But she has been shaken by the backlash against her blueprint by Tory MPs. It was not in the script. There is talk at Westminster of between 70 and 80 Tories voting against such a withdrawal deal. It could be higher if, as looks inevitable, she makes further concessions to the EU on migration and future budget payments.

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Her reaching out to Labour MPs to counteract the Tory revolt has infuriated many of her own MPs. What looked like a rare triumph for May a week ago is turning into another disaster, helped by an impeccably timed intervention by Donald Trump. His attack on May’s Brexit plans in his interview in The Sun was incendiary.

As I reported on Wednesday, May’s officials were nervous Trump might endorse his pal Johnson’s “real Brexit”. But his warning that a “common rule book” with the EU for goods and agri-foods could scupper a US-UK trade deal exceeded their worst nightmares. As did his statement that Boris would make “a great prime minister” (hint, hint). Trump’s remarkable intervention will only fuel the Tory rebellion, which will become very visible when the Commons debates the Customs and Trade Bills on Monday and Tuesday.

May’s problem is that if she retreats from her white paper, the EU talks would be dead in the water. A chaotic, damaging “no deal” exit, which May rightly wants to avoid, would be on the cards. But if she presses on with her plan, the Brexiteers’ guerrilla warfare will make her government look dysfunctional. Crucially, it now looks virtually impossible for any Brexit option – May’s deal, the hard Brexit backed by some Tories and the “no deal” exit favoured by others – to win the necessary Commons majority. They would all be voted down. May might have scraped through with 20-30 Labour votes, but the Tory rebellion is much bigger than that.

Some of her 70-80 opponents might be scared back into the fold by warnings about a Corbyn government and an even softer Brexit, but May would struggle to make the numbers add up.

With the UK heading for a cliff-edge exit with no transitional deal next March, MPs would find a way to stop the clock. The EU would agree to extend the two-year Article 50 process. But there is no guarantee further negotiations would produce an agreement the Commons would endorse.

What would happen then? Jeremy Corbyn would seek a general election. But he would need Tory MPs (or the DUP) to vote for one and I doubt very much they would hand him a golden opportunity to get to Downing Street. The Tories would probably have a leadership election but would do everything to avoid a general election. (In any case, an election might not provide a clear answer to the Brexit question.)

The same Commons arithmetic would face a new Tory prime minister. There would be only one other way to break the deadlock: refer the issue back to the people.

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Opinion inside Labour is shifting towards a referendum – members, including Corbyn’s Momentum cheerleaders; trade unions; MPs and even the shadow cabinet. Labour’s language is softening: saying the party “does not support a referendum” now does not rule it out forever. It is now wise to “keep it on the table”.

Of course, there would be a big row about the referendum question. Those who support “no deal” would want that on the ballot paper. But I suspect parliament would vote for a straight choice between the government’s deal and staying in the EU.