As the Prime Minister comes under renewed internal pressure over the issue ahead of Parliament's return on Tuesday, new ReachTEL polling shows nearly 62 per cent of people in seven Liberal and National seats across the country want Coalition MPs to have a conscience vote this year.

Mr Abbott and his supporters have warned Mr Turnbull against any such policy shift, saying it would be a "betrayal" of the Coalition's election commitments. But moderates believe after voting in favour of the plebiscite – which would have been held this month had it not been defeated in the Senate – they have discharged their duty and are now free to push once again for a conscience vote.

Mr Turnbull concedes the issue is to be discussed again in the Coalition party room.

"But I'm the Prime Minister, the government's position is that which we took to the election, which is that this issue should be determined by a vote of every Australian in a plebiscite," he told the Nine Network on Sunday.

The poll of 4742 people – in Chisholm, Corangamite, La Trobe and Murray in Victoria, Gilmore and Page in NSW, and Durack in Western Australia – shows 60 per cent of people think it's important the issue be resolved this year.

Commissioned by the Australians 4 Equality lobby group late last month, the polling also finds 41 per cent of respondents are less likely to vote for the Coalition if it continues to block its members from a free vote.

Support for a free vote was strongest in the Victorian seat of La Trobe, held by backbencher Jason Wood, at just under 68 per cent.

But even in the seat with the least support – Sarah Henderson's Corangamite – more than 57 per cent were still in favour of a free vote.

Most of the polling was done in seats where the sitting member is on the record as supporting same-sex marriage. However, in Gilmore, where Liberal Ann Sudmalis has not revealed her stance on same-sex marriage but has previously dismissed it as a "side issue", support for a free vote was at 57.5 per cent.

Australians 4 Equality director Tiernan Brady said it was "absolutely not true" that Mr Turnbull would be breaking a promise if he allowed a free vote.

"In the last Parliament Tony Abbott made clear that that would be the last Parliament where marriage equality would not have a free vote and that was what the Coalition went to the election with," he said.

"The Liberal Party has a long tradition of the principle of members having free votes on issues they feel strongly about. That tradition should be upheld – there is no reason why on this one issue they don't get a free vote."

Co-chair of Australian Marriage Equality Alex Greenwich said it was time to get the change across the line.

"This is a straightforward reform about fairness, and people across the country want it resolved through a parliamentary vote this year," he said.

Backbenchers, including Dean Smith, Tim Wilson, Warren Entsch, Trent Zimmerman and Trevor Evans, are among the MPs arguing for the free vote. But it's understood there is also solid support for a free vote inside Mr Turnbull's cabinet.

Mr Wilson told ABC television on Sunday that when a senate committee examining same-sex marriage laws reports, "when that inquiry is concluded, obviously there is going to have to be a discussion".

"Nothing to do with me pushing for anything or anybody else."

Environment Minister Josh Frydenberg said he expects Labor to succumb to pressure and support a plebiscite.

"I actually do think the Labor Party will inevitably blink on this issue because if they're serious about giving people of the same sex the opportunity to marry, then the best way to do that is through a plebiscite to allow people of all political persuasions and of all differing views on this issue an opportunity to have their say," he said.

But his opposition counterpart Mark Butler dismissed that claim, saying a free vote was Labor's "unshakeable position".

The polling coincides with a major new advertising campaign from A4E, which will include a television ad blitz across all channels and a far-reaching billboard and digital advertising campaign.

Politicians will be confronted with billboards when they arrive at Canberra airport for the start of Parliament.

The campaign will focus on real people – soldiers, doctors, nurses, lifesavers and firefighters – who cannot marry the person they love in the country they serve, said Mr Brady.

Mr Turnbull is a supporter of same-sex marriage and has in the past been a strong advocate for a free vote. However, he adopted Mr Abbott's policy for a national plebiscite, seen by many as a delaying tactic.

with AAP