One of the many over-familiar features of the Liberals’ present leadership crisis is the role played by a well-timed opinion poll in cranking things up a notch.

Hard on the heels of Friday’s panicked back-down on the National Energy Guarantee came an Ipsos poll for the Fairfax papers that recorded a blowout in Labor’s two-party lead from 51-49 to 55-45, together with a 10% increase in Malcolm Turnbull’s disapproval rating.

The proximity of these events gives a misleading impression of cause and effect, but the poll was in fact conducted between Wednesday and Saturday, meaning any damage it recorded must have been suffered by the government beforehand. Indeed, similar movements in Turnbull’s ratings in last week’s Newspoll suggest the collapse in his personal standing predated the NEG crisis, and can instead be traced to the disappointments of the Super Saturday byelections on July 28.

However, Newspoll differed from Ipsos in finding the Coalition all but holding its ground on voting intention, which seemed to follow Turnbull’s downward turn only with last week’s outbreak of disunity.

As such, the push for Dutton looks as much a case of polls being led by a leadership challenge as the other way round.

The disconnect between the now-concrete Dutton-for-PM project and how the public sees things is illustrated by the chart below, recording Essential Research’s preferred Liberal leader polling since Turnbull became Prime Minister in September 2015, together with a trend measure of Turnbull’s approval rating.

Turnbull’s preferred leader scores have moved in tandem with his variable approval ratings, but he has consistently held the lead since the start of his prime ministership (and indeed since Tony Abbott’s position collapsed after his government’s disastrous first budget in 2014).

Separating Turnbull from the conservative insurgents are daylight and Julie Bishop, who has been the alternative Liberal leader of choice since Abbott was dumped.

What has remained for Abbott and Dutton can only be described as a rump: a constant 10% or so for Abbott, and barely half that for Dutton since the pollster first felt it worth including him as an option in March last year.

In explaining all this away to potential party room supporters, Dutton boosters will be leaning heavily on the tactical significance of his home state of Queensland and its extravagant endowment of marginal seats — not least Dutton’s own.

The argument that a home ground advantage in Queensland would be a handy asset can be made with reference to Kevin Rudd’s performance in 2007 (albeit that the magic eluded him in 2013), and also to Labor’s showing in Western Australia under Kim Beazley in 1998 and 2001 – its two best results there in the past three decades.

The other aspect of the Coalition’s Queensland problem is One Nation, whose strength was largely responsible for their humiliating failure to crack 30% in the Longman byelection.

Whatever else may be said of Dutton, he is well positioned to win back these voters, and to add some ballast to the demoralising Coalition primary vote in doing so.

However, none of this adds up to a compelling argument for change: any Queensland dividend from Dutton must be balanced against his pronounced unpopularity in the southern states, and votes lost to One Nation were largely coming back as preferences anyway.

Ultimately, the case for change can only rest on faith in the destructive power of a combined Dutton-Abbott assault on Labor – a far more dubious proposition in government than it might have been from opposition.

What do you think Dutton’s chances are with the electorate? Write to [email protected] and let us know.