Focus groups in western Sydney and Melbourne were unanimous that Mr Turnbull had failed to achieve anything for them and showed deep frustration. "If he just had the guts, the political will," said a younger voter from Melbourne, reflecting a widely held view.

Said an older voter in western Sydney: "He just needs to grow, pardon me, balls." Another said: "We've switched off."

The research by Ipsos conducted last week for Fairfax Media found a "strong consensus" that Mr Turnbull "has sorely disappointed", according to Ipsos research director Laura Demasi, who moderated the Sydney groups.

Tony Abbott was not cited as an alternative and was criticised by many as a wrecker, but he was nominated by some voters, unprompted, as a leader who had achieved more. Said one Melbourne man: "Abbott did what he said. Turnbull hasn't. It's the Julia Gillard disease."

Among the four groups of undecided voters, two each from marginal electorates in Melbourne and western Sydney, Opposition Leader Bill Shorten was not seen as an attractive option, either.

The distaste for both major parties did seem to create an opportunity for the minor parties; One Nation leader Pauline Hanson and independent senator Derryn Hinch were praised for speaking their minds. Some voters named the Greens as a potential alternative yet none could name the party leader, Richard Di Natale, nor his predecessor.

Same-sex marriage was not a top priority among most in the groups, but it did emerge as a current example of the Prime Minister's perceived inaction.

"Do something, like same-sex marriage," said a younger Melbourne participant. Regardless of individual voters' views on the issue, she said, it was important that Mr Turnbull "just do something".

A woman in the group of older voters in western Sydney said: "John Howard was able to change the Marriage Act it in an afternoon," when he defined marriage as an act between a man and a woman. "Why is it taking us 15 years to change one word?"

When asked to name anything that Mr Turnbull had accomplished in nearly two years as Prime Minister, people in the groups were unable to name anything that affected their lives.

They were able to nominate only a single decision - a rearrangement of government agencies for the pending creation of the Home Affairs department.

Ipsos surveyed four groups in all, two in each city. The Home Affairs decision was mentioned in two. In the other two, participants could think of nothing at all.

And among the group of voters aged under 45 in Sydney, Mr Turnbull's high-profile recent announcements on national security and terrorism were greeted with "absolute cynicism about the real threat of terrorism in Australia amongst the 20 somethings," as Ms Demasi put it.

"There was such a strong consensus in this group of the idea that the threat of terrorism in Australia is seriously overblown and is being manipulated to the benefit of the government, namely as a source of distraction from other issues. I was blown anyway by this - I've never seen this before."

A younger western Sydney voter said terrorism was used as a political distraction: "It's like smoke and mirrors - 'look over here while we ruin your lives over there'."

And another: "My friend is terrified to catch the bus. Why do they want to make you feel like that?" A third said: "They are instilling fear. Leave it out of the papers - just do it behind closed doors."

Asked by the moderator whether Islamic State were a real threat, the eight voters around the table shook their heads. One man remarked: "One person a year dies of terrorism, less."

A woman added: "I don't want to say they should spend less money on terrorism because they seem to be doing a good job, but I don't think they should concentrate on it so much."

Among older voters, however, terrorism was nominated as a real concern; some voters linked it to the issue of border control. Among other issues, the long-standing concerns over health care, education and government debt were overtaken by a surging new one - housing affordability.

In the western Sydney groups: "They agreed that Shorten is not an appealing alternative, even amongst 2016 Labor voters, who believed he could not be the leader they were looking for - but had no idea who could," Ms Demasi observed.

It was not much better among the Melbourne groups, although one voter said that Mr Shorten was "more in tune with me and my needs".

A participant in the group aged over 40 said: "Trust, he's a snake."

Both main parties were held in disdain for "chopping and changing" their own leaders: "They get in and hardly have time to warm the seat and they're looking to topple them," said one voter. "We thought the Liberals were better than that, but they're just as bad," remarked another.

Sydney's first focus group contained undecided voters aged over 45, who voted Liberal in the last federal election, while a second group had undecided voters aged 18-45 who voted Labor in 2016.

In Melbourne, the first group included undecided voters aged over 45 who voted Labor last year, with the younger focus group had those who voted Liberal in 2016.