Peter Dutton is trying to reboot his leadership before a byelection test as a new poll has Liberals questioning the party’s direction.

An Essential poll published in The Guardian on Tuesday showed Mr Dutton falling into third place (behind Greens leader Adam Bandt) as the leader viewed more favourably by women voters and those younger than 55.

In seats lost by the Liberals to teal challengers at last May’s election, such as Goldstein, Kooyong, North Sydney and Wentworth, 53 per cent of voters were women.

“I can’t see us winning (those seats) again in my lifetime,” said one of the Liberal MPs defeated after a teal challenge last May.

One Liberal asked if Mr Dutton’s leading role in the ‘No’ campaign was likely to compound his demographic problem.

This week a Newspoll found support for the referendum is 10 percentage points higher among women and highest among voters aged 35 or younger.

Essential’s Peter Lewis said Mr Dutton’s fall to third place showed he had not done much to win back the demographics that had deserted the Liberals.

“Their main strategy has been not to bleed votes to the right,” he said. “It’s curling up into a metaphorical ball.”

Mr Bandt overtakes the Liberal leader at a time when his profile is rising as the Greens are locked in a fight with the government on housing policy. Voters aged 35 and under viewed him more favourably than Mr Albanese.

The next test of Mr Dutton’s electoral viability is the Fadden byelection on July 15.

Launching Labor’s campaign on Tuesday night Prime Minister Anthony Albanese linked Mr Dutton to the seat’s outgoing MP, until recently the Coalition spokesman on financial services.

“Stuart Robert is resigning from parliament having presided over one of the most shocking and cruel failures in the history of Australian politics – Robodebt,” he said.

“Ripping the humanity out of human services. Stripping the social justice from social security. Targeting vulnerable people and bragging about it.”

The Fadden contest follows Mr Dutton’s historic loss in the seat of Aston earlier this year.

Mr Dutton tried to use the Voice referendum as a launching pad for an attempt to start campaigning on the economy.

“(Prime Minister Anthony Albanese) is obsessed in relation to the Voice and other issues, and I think he’s taken his eye off the ball on economic policy and I think Australians are paying the price for that,” Mr Dutton said.

His loss in the Aston byelection in April was the first time in a century the government had won a seat from an Opposition at byelection.

On Tuesday he was more careful about his chances in Fadden, which the Liberals hold by more than 10 per cent.

“Byelections are always tight contests and the Labor Party will have all sorts of dirty tactics and smear campaigns, and I think we’ve got a great candidate, a good story to tell,” he said.

Last week was the launch of a makeover for the Opposition Leader in the form of a video about his gentler side.

The Peter Dutton We Know features testimonials from friends who call Mr Dutton “a big gentle giant”.

Liberal strategists are closely watching declining levels of household savings, insiders say, which they believe will soon fall to levels that will have voters focused on the economy.

But one Liberal MP said they had abandoned hopes for the next election some months ago in favour of a two-term strategy.

“Wait for (former treasurer Josh) Frydenberg, basically,” the MP said.