May seems to think she can go on and on. But she’s running out of road

Her face was as impossible to read as ever. Theresa May betrayed so little of her emotions as she emerged from Downing Street to unveil her Brexit deal on Wednesday night that with the sound off, you wouldn’t have known if she was resigning or declaring peace in our time.

But perhaps she didn’t quite know herself. Only minutes earlier, her Brexit secretary, Dominic Raab, had told the Conservative chief whip that he would be quitting, although his resignation was only formally accepted the next morning. She must have known this fragile truce couldn’t hold, that cabinet ministers who had lost the fight inside the room were now taking it outside. This was a prime minister with power slipping through her fingers.

Yet even in what may be her last days in office, May still has her uniquely stultifying ability to drain a moment of its drama. Ministers sometimes complain that she chairs cabinet meetings, rather than leading them; that her own views remain oddly opaque. There was a flavour of exactly that detachment when she came to parliament on Thursday morning. With ministers dropping like flies, she didn’t even try to pretend this was the deal anybody had wanted, although it does at least tick the boxes of ending freedom of movement and minimising economic disruption. Rather, she wanted the nation to know that she had done her best in trying circumstances, and if some felt it wasn’t good enough then that was regrettable but – well, there it was. The overall air was of a postwoman plodding through a blizzard, just trying to deliver what the people had ordered, as if her own feelings barely mattered. And perhaps, in a way, they don’t.

Years ago, when May first started being seriously discussed as a future leader, Europe was the one issue on which even her closest political allies couldn’t be sure where she stood. The best they could offer was that she didn’t seem terribly interested. (There is a ring of truth to former aide Nick Timothy’s charge that deep down she never believed Brexit could work, although he is wrong to suggest that if only she had believed harder in fairies everything would have worked out; if anything, she merely comes across as rather more in touch with reality than he was.)

But whatever she feels deep down, it is not the May way to emote, any more than it is to inspire. She prevails by grinding people down, wearing them out, pointing out the lack of a better alternative; it’s how she became leader in the first place, how she has survived despite her party’s misgivings, and evidently how she will now seek to stave off the attempted leadership challenge now under way.

This time she could hardly get away with pretending that nothing had changed, but the message was that nothing will be changing; the deal is the deal. Her best hope is to persuade her party that anything is better than the risk of accidentally installing Jacob Rees-Mogg in Downing Street, before somehow trying to sell her unloved deal to the nation on the grounds that at least this way everyone will know where they stand and Brexit will be over. The British people, she insisted at an almost unnaturally calm press conference, just want her to “get on with it”. Perhaps she is banking on what the academic Rob Ford calls “Brexhaustion”, or the fact that for every man or woman glued to every twist and turn there is probably one who barely cares now how this thing ends, just so long as it ends.

Yet that end now looks a very long way off indeed. There is something almost wickedly disingenuous about continuing to pretend, at this moment of great national jeopardy, that with the right person in charge we could swiftly extract a deal offering exactly the same advantages as EU membership but with none of the tiresome obligations. It is no more credible that Jeremy Corbyn, a man who can barely get through a TV interview over Brexit without contradicting his own party’s policy, could pull this mythical sword from the stone than that Boris Johnson or Rees-Mogg could.

If negotiations have truly reached a stalemate, then stopping the clock on article 50 and throwing the ball back to the people in a second referendum arguably seems the fairest way forward. Having never personally been convinced of the case for a people’s vote, nonetheless I’d bite your arm off for one if it’s a choice of that or crashing out without a deal, a scenario in which the health secretary apparently cannot guarantee that lives would not be lost. The more real the prospect of no deal becomes, the more pressing the case for seeking consent, no matter how resistant both May and Corbyn are to the idea.

But let’s not pretend that the outcome of a second referendum would necessarily be any more welcome than the last one, that the losing side would be any more reconciled to defeat, or that we wouldn’t spend the next 10 years arguing about who lied and cheated. And before we get to any of that, the last act of the Tory psychodrama must first play itself out. May is not just running out of road on Brexit. Relations with the DUP, which won’t back her deal, have descended into the deep freeze amid mutterings of private promises betrayed. She surely can’t rely on their votes now to drive through whatever tattered fragments of her domestic policy are left.

Desperation to keep the Brexit show on the road is now bending the rest of government out of shape, with rumours of policy and spending decisions being twisted to keep restless ministers on board. She could see off the Rees-Mogg charge but survive only as a puppet leader, her strings jerked by any Brexiter willing to stay in cabinet – a deal Michael Gove seems to have initially offered her. It seems unlikely that any domestic legacy of her own could be salvaged from such wreckage.

But if her premiership has been sorely lacking in imagination at times, by taking the referendum result so literally she has at least provided a moment of dreadful clarity about the consequences. Tory Brexiters demanded the impossible. Well, now they have it; a deal impossible to get through parliament, impossible to sell to leave voters so cynically led to expect something better. If nothing else, history will surely remember her more kindly than either the architects of leave or her predecessor, David Cameron, whose catastrophic error of judgment landed us in this mess. They broke it, but she owned it, which explains the odd note of pity that creeps in when her name crops up in conversations beyond Westminster. It may now be for someone else to glue the pieces back together.

• Gaby Hinsliff is a Guardian columnist