Men in every age group have shifted their opinion on gay marriage – mainly opposing it in 2005 to generally supporting it in 2015.

New data from the long-running University of Melbourne HILDA study shows a profound shift towards the view that homosexual couples should have the same rights as heterosexual couples.

“In a sense that debate has kind of been won in terms of community attitudes, it just seems that the political system hasn’t caught up,” says study author Professor Roger Wilkins.

The Household, Income and Labour Dynamics in Australia survey interviews the same 17,000 people each year on a range of issues.

The proportion of women agreeing with a shift to equal gay marriage rights rose from 43 per cent in 2005 to 67 per cent in 2015.

Among men, the proportion rose from 32 per cent to 59 per cent.

Melbourne University gender studies lecturer Dr Hannah McCann said it was the biggest shift in the marriage, children and parenting section of the survey.

“We have seen during that time period, from 2005 to 2015, so many countries around the world change their laws around marriage equality,” McCann said.

“I think that we can surmise that this has had some impact, the campaign has had some impact.”

McCann said there was a slightly smaller change in older age groups.

“But overall everyone was changing towards the agreement end,” she said.

Young men aged 15 to 24 had the biggest positive shift.

Meanwhile in Canberra, Prime Minister Malcolm Turnbull faces internal strife over a new push within his party for a defining vote on the issue in Parliament.

Conservative senator Eric Abetz insists the government must hold a national plebiscite on same-sex marriage but won’t say whether he will be swayed by its outcome.

Turnbull is facing calls from within the Liberal Party to take a second stab at securing parliament’s approval for a plebiscite on same-sex marriage.

However, there is also pressure for a partyroom meeting next Tuesday to discuss a private member’s bill being proposed by a small group of Liberal backbenchers.

Turnbull has reportedly called two of those MPs – Queensland’s Trevor Evans and Western Australia’s Dean Smith – urging them to support the government’s plebiscite policy.

But News Corp said the two men were sticking with their plans.

Another pro-marriage proponent, Warren Entsch, told News that he was prepared to continue even if the right continued to threaten Turnbull’s leadership.

Abetz, a staunch opponent of same-sex marriage, refused to commit to taking heed of a plebiscite if the overwhelming majority of Australians were in favour.

“I think it is appropriate that the minority view, whatever that may be, is still expressed within the parliament,” he told Sky News on Tuesday night.

Abetz said Coalition MPs crossing the floor on same-sex marriage would be “exceptionally grave” for the Turnbull government.

“What it would tell the Australian people is that the government has lost its authority, has lost control on the floor of the house,” he said.

“Any of my colleagues that might be contemplating such action should be thinking about this not two or three times, but a dozen times, and then come to the conclusion that losing government is not worth it.”

The prime minister has told reporters in Perth the government’s position is clear.

“We made a commitment to give every Australian a say on this issue and that is our policy – it has not changed,” Turnbull said.

Assistant Minister Alex Hawke says it would be good for the government to resubmit the bill to the Senate and urge crossbenchers to look at it again in the light of strong public support.

Queensland Liberal MP Andrew Laming says the government should remain focused on delivering a plebiscite.

A voluntary postal vote – which did not require legislation – was a “highly worthy option” and likely to be cheaper.

Cabinet minister Peter Dutton, who favours the postal vote model, says it is time for the issue to be dealt with “behind closed doors”.

“Now is the time for people, having had their say, frankly to contain their comments until they get back to the party room. That’s where the Liberal Party has our best discussions and our best debates,” he told FIVEaa radio in Adelaide.

One of the supporters of a private bill, Victorian Liberal MP Tim Wilson, has told colleagues and local branch members he could cross the floor of parliament.

However, he would not back a Labor version of the same bill.

Other Liberal backers could include Trent Zimmerman from NSW.

– AAP