Many Labour supporters are quietly allowing themselves to celebrate: if Liz Truss does win the Tory leadership, a Labour government, they think, is much more likely. It may well be so. Among the general public, Truss is on many measures the least popular of the last three Conservative contenders who fought it out last week. YouGov found that even Tory members preferred Kemi Badenoch and Penny Mordaunt to the Foreign Secretary.

The reason is obvious, and personal. Truss comes across as by turns slightly eccentric, a bit vacant and – well, there’s no easy way to say this – just a tad weird.

Truss has failed to win over even a third of Conservative MPs to her cause, seems to have failed to impress most colleagues as Foreign Secretary, and is no-one’s idea of a sharp debater or impressive public speaker. Only the arcane strangeness of our blended constitution, suspended somewhere between Parliamentary democracy and a direct democracy led by members, could put her in No. 10.

But, as usual, there’s room to at least raise some doubts about this received wisdom. So many prime ministers have surprised in office that we’ve got to at least entertain the possibility that Truss might be an unexpected hit in No.10.

Ted Heath had immersed himself in policy, and management techniques, before he took office in 1970: if stiff and not particularly popular, he seemed serious and credible. But it all fell apart in short order. Gordon Brown was an intellectual heavyweight, a tough operator and a very experienced chancellor. Within months, his aura of invincibility had been stripped away.

On the other hand, Margaret Thatcher was seen as something of a joke when she outmanoeuvred her party’s big beasts to seize control of the Tories in 1975. Her opponents eventually had their laughter stuffed back down their throats. You never do quite know how anyone will do in really high office. They don’t even know themselves.

So it’s at least possible that Truss will surprise on the upside. Indeed, the chatter in Westminster and Whitehall places the bar so low for her that it’s likely she’ll step (though perhaps not leap) over expectations pretty easily.

After all, any prime minister can deploy enormous inbuilt advantages. They control the Government’s agenda. They are able to brief the press, placing campaigns, stories and ideas where and when they want.

New leaders almost always receive some sort of bounce in the opinion polls, too, as ex-loyalists return home after scandals and recriminations, and more uncommitted voters not unreasonably give a relatively fresh face a chance to see what they can do.

Combine the two, and anyone moving into No. 10 can feel the wind at their backs. It will help Truss in this respect that chunks of the legacy print press – especially the Daily Mail, key to her appeal at the moment among members – seems very strongly behind her.

Consider, also, her strategic positioning. She is making absolutely clear that she will slash taxes, at a time when many voters in every income group feel very squeezed indeed by some of the highest taxes they have known for decades.

That populist appeal to keep money in people’s pockets is likely to chime much more with an age of big promises (and small delivery) than Sunak’s belief in budgetary responsibility – deferring income, yet again, for employees who have not seen their wages rise since before the Great Recession.

Sunak can easily be painted as a rich man playing at politics, committed not so much to struggling workers as to his own rather smooth and over-burnished image. His slickness and fluency jar with an era when it is authenticity, not advocacy, that seems to convince.

Somehow, Truss has also managed to paint herself as some sort of ultra-Brexiteer (despite having campaigned for Remain). This will shore up her rightwards flank against any renewed insurgency by Nigel Farage, or at least prevent more votes leaking away to the Reform party.

Party management will also be easier under Truss than Sunak. Hard Brexiteers seem more willing and able to make trouble than those One Nation Conservatives that remain within the fold, and Truss seems to have convinced them that she has their best interests at heart.

Boris Johnson, nursing his wounds on the back benches, is also far less likely to take aim at Truss. She is much closer to him in outlook, and was more loyal to him near the end, than Sunak was.

All of this is meant as a corrective to conventional wisdom. In fact, Truss has shown little in the way of the vision, competence and authority she will need as she confronts Britain’s present crises. But politics also retains its capacity to surprise. So, just possibly, does Liz Truss.