And Coalition MPs are seen as out of touch with the community - and could lose votes, and even their seats - if they continue to block a free vote in Parliament and insist on the defeated plebiscite policy.

The ReachTel poll of 12 Coalition seats, commissioned by Australians for Equality, targeted Bowman, Brisbane, Cook, Fisher, Goldstein, Moncrieff, New England, Pearce, Petrie, Robertson, Swan and North Sydney. Its findings are in line with a February ReachTEL poll of seven Coalition seats.

More than 50 per cent of voters in all 12 seats said "yes" when asked if same-sex couples should be allowed to marry. A majority of voters in all 12 seats also said it was "very important" that the issue was resolved by parliamentary vote in 2017.

The findings underscore how politically unpopular the Coalition's support for a plebiscite - which Prime Minister Malcolm Turnbull restated on Friday - and opposition to a free vote in Parliament is and call into question conservative claims the issue has been settled.

Divisions emerged in the federal cabinet on Sunday after Health Minister Greg Hunt and Resources Minister Matt Canavan backed Immigration Minister Peter Dutton's call for the government to keep the plebiscite policy and warned the chief executives of some of Australia's biggest companies to "stick to their knitting" and stay out of the debate.

But Education Minister Simon Birmingham backed the chief executives' right to freedom of speech: "I see no reason as to why business leaders are not free to do so on marriage equality."

Of the 12 seats polled, four are held by cabinet ministers, with about 700 people polled in each seat.

In Treasurer Scott Morrison's NSW seat of Cook, 56.2 per cent of voters said the law change should be enacted and 32.5 per cent opposed it; 50.9 per cent said Mr Morrison should vote on the matter in Parliament and 54.8 per cent of voters strongly agreed or agreed the Coalition was out of touch on the issue.

In Deputy Prime Minister Barnaby Joyce's NSW seat of New England, 50.5 per cent of voters backed same-sex couples being able to marry, while 39 per cent opposed it; 54.7 per cent backed a vote in Parliament, and 49.4 per cent of voters agreed or strongly agreed the Coalition was out of touch on the issue. Mr Joyce opposes same-sex marriage.

In Social Services Minister Christian Porter's WA seat of Pearce, 52 per cent of people backed same-sex marriage and 35.8 per cent opposed it. Significantly, after big swings in the seat against the Liberal Party in the recent state election, 36.4 per cent of voters said they were less likely to vote for Mr Porter if the issue wasn't dealt with, with 25.1 per cent more likely to vote for him and 38.5 per cent unchanged.

And in Trade Minister Steve Ciobo's safe Queensland seat of Moncrieff, a thumping 61.2 of voters backed legalising same-sex marriage, with just 28.7 per cent opposed. Mr Ciobo supports changing the law.

Australian for Equality director Tiernan Brady said the poll reflected "what we are seeing in town hall meetings all around Australia".

"This won't go away, this doesn't need to be a political football, a clear majority of voters in every party want this," he said.

Australian Marriage Equality co-chair Alex Greenwich said the poll represented "the strongest support for marriage equality we have ever seen in Coalition-held seats".

"Whether their MP is a supporter or an opponent of marriage equality, the strong message from constituents is that they want their MP to have a vote on the floor of Parliament this year."

In Queensland, voters in Brisbane backed a law change 67.5 per cent to 23.1 per cent opposed; in Bowman, voters backed change 59.3 per cent to 33.2 per cent and in Fisher, there was 58.2 per cent support and 35.6 per cent opposed and in marginal Petrie, support for the change ran to 59.4 per cent while 32.2 per cent opposed changed.

In Victoria, the blue ribbon seat of Goldstein saw a whopping 77.1 per cent of respondents back change, with just 17.1 per cent opposed while in the key WA marginal seat of Swan, 56.6 per cent backed change and 31 per cent opposed it.

In NSW, 62.2 per cent of voters in the Central Coast seat of Robertson backed change and just 26.9 per cent opposed the law change, while in North Sydney, a thumping 70.8 per cent of voters backed change and 21.1 per cent opposed it.

Liberal moderates continue to work for a free vote before the May budget, as revealed by Fairfax Media in February, though such a move would trigger a backlash among conservative MPs.

The findings come as the Turnbull government prepares for the last two sitting weeks before Parliament rises, with the Coalition set to focus on its plan to cut company tax, pass the omnibus savings bill and debate changes to section 18C of the Racial Discrimination Act.

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