I write to a rumble of rumours that one or more members of the cabinet will quit if the prime minister tries to make a Brexit deal that is not to their liking. This adds another diabolical dimension to what has been dubbed “hell week” for Theresa May, but the rest of us ought to be able to treat these resignation threats with sanguinity. If Britain is deprived of the services of Andrea Leadsom as leader of the house, I am sure we will all do our best to cope. The nation ought to be able to contain its grief if Esther McVey quits as work and pensions secretary. It will not require bulk orders of tissues to mop up the tears shed if Penny Mordaunt resigns as international development secretary. The pity is that their fellow Brexiter, Chris Grayling, is not being talked about as a possible cabinet flounce-out. His resignation as transport secretary would be celebrated by spontaneous street parties of joyful train travellers.

The self-estimation of the importance of possible cabinet resignees is a great deal higher than the esteem in which they are held in the country. Most voters would probably struggle to put a name to their faces. Mrs May’s premiership and, with it, her nation’s future, ought not to be held to ransom by cliques of junior cabinet ministers threatening to leave if they don’t get a Brexit to their precise specifications. Yet these resignation threats will undoubtedly have an impact on the chances of avoiding a disaster because they are another complicating challenge for Mrs May as she tries to navigate her way through this morass.

That is another of the distortions to the political fabric you get when a government with no majority is trying to deal with a massively important, hugely perilous and highly combustible question. Politicians who would be very marginal, if not entirely irrelevant, in any other context have gained an inflated influence over the future of the country. So we have the Democratic Unionists, a party of just 10 MPs, and one incapable of forming a government in their own relatively small corner of the United Kingdom, talking about their “blood-red lines” and threatening to tear down the temple if they don’t get exactly what they want. Or consider Jacob Rees-Mogg. Were it not for the combination of Brexit and a majority-less prime minister, the MP for the 18th century would be little more than a comedic throwback, not the mouthpiece of a cabal dictating demands to the prime minister that cramp her ability to manoeuvre into a viable position.

Who remembers Richard Body, Teresa Gorman and Tony Marlow, three eccentric Tory backbenchers of an earlier era? Almost entirely forgotten now, they gained an exaggerated sway over events when Sir John Major was trying to get the treaty of Maastricht through parliament without a reliable majority. When he was caught referring to these Eurosceptics as “bastards”, the world was quite shocked. I guess the 1990s was a more innocent age. It wasn’t just the revelation that Sir John could be sweary when he thought the public wasn’t listening. It was also because that Tory prime minister included three of his cabinet in the bastards category.

Asked about it the other day, Sir John said that the Brexit fundamentalists who are threatening Theresa May are much worse than the Eurosceptics who endeavoured to wreck his premiership. He is right and for several reasons. For one thing, there are now many more bastards in the Tory party. In Sir John’s day, you didn’t need many fingers to count the number of Conservative MPs prepared to contemplate the destruction of their own government over Europe. The fanatical anti-Europeans are still a minority in the Conservative party and the Conservative party only speaks for a minority of Britain. That’s something that should be always remembered when the Moggites are noisily claiming to speak for the people. But they are a much more substantial minority than they were and their sense of self-importance has made them a reckless one. They strike me as more kamikaze than the Tory MPs who tortured Sir John over Maastricht. At a critical stage in the parliamentary battle, he eventually had to resort to making it a confidence issue. The EU-haters of his day liked the idea of a general election even less than they did the treaty and they backed off. One of Mrs May’s many problems is that she cannot be absolutely sure that some in her party wouldn’t risk tipping the Tories out of office. It still seems to me improbable that any Conservative MP would vote with the opposition in a way that might trigger a snap general election that could put Jeremy Corbyn into Number 10. But some of them are so addled with Brexsteria that I would no longer bet my house on it.

There are only so many resignations that any prime minister can endure

Another crucial difference is the cabinet. The Major government included the passionately Europhile Ken Clarke and the intensely Eurosceptic John Redwood. His cabinet was horribly split over Europe, but no one quit because of Maastricht. Mrs May has already lost two cabinet ministers over Brexit. There are only so many resignations that any prime minister can endure. That is one thought in the heads of those ministers menacing her with this threat. Another thought is about a future Tory leadership contest. Boris Johnson is not the only one to have calculated that quitting on the grounds that Mrs May is “betraying” Brexit might well please the Tories’ extremely Brexity membership.

There is one more crucial difference between the agonies suffered by Sir John and those besetting Mrs May. That is the state of the opposition. During the struggles over Maastricht, Labour was led by John Smith, the most pro-European leader in the party’s history. Mr Smith was a personable and guileful lawyer. His commitment to Europe did not prevent him from engaging in sly parliamentary tactics to try to defeat the government, but in the end Labour had a leader who wanted Britain to have a good relationship with its neighbours. Jeremy Corbyn is an entirely different species. He voted against Maastricht, as he did against every other EU treaty that has come before the Commons during his parliamentary career. Whatever deal Mrs May manages to come up with, it will not pass Labour’s “six tests” because those tests were designed not to be passable. So she would be sensible to assume that Mr Corbyn will attempt to whip Labour MPs to vote against whatever deal emerges in the hope that this will trigger what he really wants: the collapse of the government and a snap general election.

On the face of it, this makes it very hard to see how Mrs May can strike any agreement with the EU for which there will be parliamentary approval. The opposition has no incentive to help her out of a swamp of the Tory party’s own making. The Democratic Unionists say they will cut off their life-support. The DUP are co-ordinating with the Tory Brextremists. The parliamentary maths is a horror. Dominic Raab, the Brexit secretary, likes to tell friends that he has “the second worst job in government”, the worst being that of chief whip, the man who is supposed to magic together a majority for Mrs May.

The fragility of her position will be both help and handicap when she meets European leaders in Brussels this week. It assists her a bit because they fear that the termination of her premiership could leave them facing someone even harder to deal with or, worse, a Britain so chaotic that it is incapable of concluding the negotiations at all. Her weakness doesn’t help Mrs May because there is less incentive for European leaders to make concessions and, in the process, spend some of their own political capital, if any agreement is just going to be voted down by the British parliament anyway.

The difficulty from the very beginning has been how to find an arrangement that simultaneously worked with the EU, satisfied the Conservative party and was capable of commanding a majority in the Commons. One way of looking at the last 28 months of Brexit torture is as a protracted and painful education in the impossibility of finding a satisfactory solution to this conundrum. Another way of looking at the last 28 months is as a long and expensive education for Britain that any deal is going to be suboptimal, because there is no deal with the EU that is better than the terms we currently enjoy as members. Any number of cabinet resignations are not going to change that.

• Andrew Rawnsley is an Observer columnist