Today’s papers bubble and seethe with stories about David Davis and the Conservative leadership. Since Tory MPs are “the most sophisticated electorate in the world” (to put it euphemistically), these may well not all come from his supporters. If you are ambitious, perhaps feel overlooked, and have attached yourself to an aspirant – Boris Johnson, for example – it is in your interest to suggest to journalists that some other potential candidate is seeking to bring down Theresa May and replace her. Let the Brexit Secretary get the blame for disloyalty, rather than the man you support.

None the less, there can be no doubt that Davis has backing within the Parliamentary Party and among the party membership: he topped this site’s future leader survey last week, for example, though far from overwhelmingly or convincingly. His backing seems to be coming from two groups of people. The first are those who believe he should become Prime Minister and lead the Conservatives into an election in 2022 or earlier. The second are those who think that he should go to Number Ten as a caretaker only, stepping down when Britain leaves the EU in the spring of 2019. He would then make way for one of the mass of Ministers, both from within the Cabinet or without, who believe that they themselves should be party leader.

That latter group is obviously a fractured one: potential leadership candidates who have been named in the press since the election include Philip Hammond, Amber Rudd, Michael Gove, Sajid Javid, Priti Patel, Andrea Leadsom, Rory Stewart, Jo Johnson, Dominic Raab and Jesse Norman. Not all of these names could make a run-off; quite possibly none of them would. Andy Warhol’s famous saying hovers over some of the names on this list: “in the future, everyone will be world-famous for 15 minutes”. And the size of the former group – that’s to say, those who back the Brexit Secretary on his own merits – is an unknown: in these febrile conditions, it is hard to be sure. Both seem to be angling for a “coronation”, whereby Davis becomes Conservative leader and Prime Minister without Party members having a say.

This shifting cast and these mixed motives help to explain why this prospect, which is not without its attractions at first glance, turns out on closer inspection to be deeply problematic.

First of all, coronations do not automatically confer legitimacy, nor have they turned out well in the recent past. Theresa May was crowned without a vote by the members, which meant that her distinctive programme of ideas went unchallenged: energy price caps, workers on boards, more council houses, an industrial policy. It would have been better had these policies been tested by the members before being put to the voters. Furthermore, confidence of the membership in the leadership is not high. Our survey found that the real front-runner wasn’t the Brexit Secretary at all: it was “none of the above”. Members might not rally behind a new leader who they felt had been foisted on them. And there are not now so many members that Conservative MPs can take them for granted – far from it, as the lack of them on the ground in last month’s general election campaign proved.

Second, there doubtless wouldn’t be a coronation in any event. Boris Johnson would not sit idly by, and watch someone else stroll off with the prize he covets. A candidate who backed Remain in last year’s referendum would presumably also emerge – or more than one. Britain could be presented not with a stately coronation, but a garden party dust-up. This would be unlikely to boost Tory ratings. Third, Davis might not win out after all. He has been here before – as a front-runner in the Conservative leadership stakes at a time when the party was yearning for change. That didn’t work out well for him. This time round, he is 68 – twelve years older. He would be 73 in 2022. Were he to be leading the Tories then, he would be asking to serve as Prime Minister until he is approaching 80.

The familiar charge-sheet would also be recited against him: too right-wing…it’s DD for me…called a weird by-election…part of the past…pushed for last month’s early election which duly went wrong. Much of this, including the claim that he doesn’t put the hours in, is deeply unfair. The Brexit Secretary is a politician of the first rank, and the cult of youth has been over-sold. But there must be a presumption that the Tories will need a game-changer if or when May leaves Number Ten. And it is reasonable to ask whether a familiar Conservative face could make that happen. Davis seems to take the point. There is no sign that he himself is seeking to destablise May – a move that could, were it to go wrong, weaken the Government’s foundations and advance Jeremy Corbyn’s position.

Tory MPs are damned if they do and damned if they don’t. If the Prime Minister is deposed, the after-shock could produce an election, lost seats, and a Momentum majority. If she stays, the Government risks becoming a ghost ship, at the mercy of the winds and tides. Under such circumstances, it could collapse altogether: voters might then resolve to throw the dice and let Corbyn have a go. On balance, the best course as matters stand is slowly to seek to rebuild May’s position, at least for the moment.

Davis has plenty to be getting on with. There is the Brexit negotiation. There is the Repeal Bill – which embodies the paradox of seeking temporarily to preserve the EU status quo while simultaneously being targeted by Remain MPs. It is to be introduced this week. The Brexit Secretary’s best course is to continue to cool his more hot-headed supporters, and hope that the summer recess brings, if not recovery for his party, then at least respite. Then the work of reconstruction can, with a bit of luck, kick off at party conference.