‘The numbers just don’t stack up,’ one cabinet minister wearily declared to me on Monday night. This is, perhaps, the single most important fact in British politics today: Theresa May does not currently have the votes to pass her Brexit plan even if she could get the European Union to accept it.

Boris Johnson and David Davis’s resignations mean that it won’t just be Jacob Rees-Mogg and a dozen ultras voting against Theresa May’s Brexit deal, but a far larger group. Further proof of this came on Tuesday, when two of the party’s vice-chairs — Ben Bradley and Maria Caulfield — resigned so that they could oppose the deal. Tellingly, neither one would have been on anyone’s list of Brexit obsessives. When I asked a Remain--voting cabinet minister where things will now end up, he predicted that there would be ‘60-odd voting against’ Mrs May’s compromise, ‘and you can’t make up for that with pragmatic Labour MPs’.

Boris Johnson’s resignation letter was free of classical analogies. But one would have been appropriate. For what Mrs May appears to have won is a Pyrrhic victory. She has got the cabinet to agree a common position that looks like it will open the door to negotiations with the EU. But the price she has paid for this success will result in so many Tory MPs voting against the deal that it is difficult to see how it can pass.

Part of the problem for Mrs May is that many Tory Eurosceptics think that if her deal is defeated, Britain will simply default to leaving the EU without a deal. They see the choice as being between Mrs May’s deal and leaving without a deal and trading on World Trade Organisation terms. Indeed, one of the things that led to Boris Johnson’s resignation was his conclusion that no deal would actually be preferable to the Chequers plan. As this group are quick to tell you, the House of Commons has already paved the way for a no-deal Brexit by voting to trigger Article 50 and start the two-year process of formally leaving the EU.

This is technically true. But it misses the political realities of the situation. Barely one in ten MPs supports the idea of a no-deal Brexit, and it is certain that the House of Commons would try to foist another solution upon the government. However chaotic the process, an alternative would be found.

But we are getting ahead of ourselves. The first question to ask is whether Mrs May will survive as Prime Minister until Brexit Day, 29 March 2019. May loyalists are bullish about her prospects. They point out that she has weathered the departure of two of her most senior cabinet ministers with remarkable sangfroid. They also say, rightly, that there have been remarkably few people agitating for a leadership election.

At the moment Jacob Rees-Mogg, the leader of the European Research Group, the key lobby of Brexiteer Tory MPs, keeps saying he wants to change the policy, not the Prime Minister. But it’s increasingly clear that you can’t do one without the other. As one cabinet minister tells me, ‘she desperately wants a deal’ and she regards the Chequers plan as a crucial step towards that. Those around May know that if she abandoned this plan, she would lose face at home and all credibility in Brussels.

But even if Brexiteer Tories decided to try to remove Mrs May, they wouldn’t succeed. They probably do have the numbers to get the 48 letters which would force a vote of confidence, but they definitely don’t have the 159 votes they’d need to win it. Matters are further complicated by the fact that if Mrs May won a vote of confidence, she couldn’t be challenged for another year. Interestingly, one of those closest to Mrs May believes that a confidence vote might, in fact, benefit her, as she would win it comfortably and then have a year without the threat of another one, giving her a freer hand in the Brexit negotiations. Her critics agree. As one cabinet member puts it, ‘If an attempt is botched, she’ll be in the constitutionally unprecedented situation of being a prime minister who cannot be removed by her party.’

Some Brexiteer Tories think it best to wait until September to dislodge her. Their logic is that the EU will be asking for further concessions by then and they calculate that Mrs May will oblige. If she caves on the two issues that the voters care about most keenly — money and migration — then a confidence vote could finish her off. But others argue that by September it will all be too late. They contend that a new prime minister, installed now, would have a chance of getting Britain ready to leave the EU without a deal by March next year. Wait until the autumn and Britain will be forced to take whatever the EU offers.

Of course not all Brexiteers are against the Chequers plan. Some accept it as a necessary staging post to a cleaner break in years to come. This group, the so-called hedgers, agree with Michael Gove that the single most important thing is to get out of the EU now, while we still can, and then worry later about how to fix the relationship. The challenge for this group, however, is to persuade their own side to be extremely pragmatic and accept a diluted Brexit for now.

One close ally of Gove likens him to Michael Collins, one of the founders of the Irish Free State. Collins took part in the Easter Rising, was one of those who declared Irish independence, and fought in the war that followed. But in 1921, he signed a peace treaty with the British that granted Ireland ‘dominion’ status under the crown. This fell far short of the republic that many in the IRA wanted. But Collins felt that the treaty was worth it as ‘it gives us freedom, not the ultimate freedom that all nations desire and develop to, but the freedom to achieve it’. The signing of this treaty led to an Irish civil war that claimed Collins’s life. But gradually Ireland did become a fully self-governing nation, becoming a republic in 1948.

Gove and his fellow ‘hedgers’ are unlikely to be able to persuade every Brexiteer MP that such a big compromise is worth it — especially when so many are convinced that the alternative is a no-deal Brexit. For these reasons it is almost certain that Mrs May will need votes from the opposition benches to pass her deal. This is a problem for her because, as her chief of staff Gavin Barwell has emphasised in the past, Labour will vote for the option that causes the most grief to Tories and will never pass up the opportunity to bring down a Tory government. Opposing the deal also makes it easier to keep Labour united, since everyone can have their own reason for voting against it.

In the past when No. 10 have been worried about the numbers on their own side, they have sought to woo Labour moderates. Think back, for example, to before military action in Syria. But Labour centrists tend to be pro-European. They wouldn’t want to vote for May’s deal as they’d calculate that its defeat might bring down the whole Brexit process. And who now would rule out Brexit being delayed or even abandoned?

One former cabinet minister tells me that the two likeliest outcomes are now ‘no deal or no Brexit’. The chances of a second referendum have also increased; it is one response to a deadlocked parliament, and no Tory wants an early election. In No. 10 they have long thought that if Mrs May’s deal was rejected, parliament would park Britain in the European Economic Area and a customs union with the European Union. This would effectively leave Britain as a non--voting member of the EU.

None of these are good options. Even with the most rigorous preparation, no deal would create significant economic uncertainty. Given the paucity of the government’s work on it, there would likely be an economic shock. But no Brexit would cause a democratic shock — and these are harder to recover from than economic shocks.

Taking the EU’s preferred options — staying in the customs union and the EEA — would rightly be seen as contemptuous of the referendum result. And if there were to be a second referendum, what would the question be? Leavers would say: deal or no deal. Remainers would say: Mrs May’s deal, or cancel Brexit. One thing is certain: it would be impossible to devise a question that would satisfy everybody. The referendum would only end up creating more division, not to mention a sense of outrage among those who did not get the question they wanted.

This is why a deal would be best. The Chequers plan is flawed. But given how little progress the talks on the future relationship have made, some of the ideas in it are reasonable. Sticking to the European rulebook on goods is not such an onerous undertaking, given that standards on them are increasingly global. But the same is not true for food and drink, which is why it’s so unwise for Mrs May to volunteer to have the agri-foods industry operate under standards set in Brussels. Countries such as Australia and the US vary wildly on food regulation and it will be harder to strike a free trade deal with either for as long as Britain is signed up exclusively to another food regulation regime.

On customs, it remains hard to imagine how the EU would be prepared to have a third country collect tariffs on its behalf — especially given that the Commission gets to keep 80 per cent of all the tariff revenues collected. But some of the proposals in it are sensible given where the UK now finds itself.

The Brexiteers are right to be furious about May’s mistakes. Ruling out cameras on the Irish border meant that it was never going to be possible to use technology to help solve that problem, meaning that the United Kingdom would be faced with a choice between staying in the EU’s regulatory orbit or putting up an internal border. An equally big error was the failure to put sufficient energy and resources into ‘no deal’ planning. This was always going to limit her options: anyone in a negotiation who can’t walk away is in a weak position. These gross strategic errors are infuriating. History will not absolve her.

But what’s done is done, and Brexiteers need to accept this. The talks have been terribly mishandled, the basic rules of negotiation have not been followed, a Tory majority has been blown in a needless election, and the Prime Minister is now at the mercy of the EU and parliament. In short, Britain is in a hole. What matters now is finding a way out.

Some Brexiteers accept the Chequers plan as a necessary staging post to a cleaner break in future

Spectator.co.uk/podcast James Forsyth, Paul Goodman and John Springford on what May should do next.