The "silent majority" of Australians will reject moves to introduce same-sex marriage, according to the Abbott Government frontbencher responsible for social cohesion.

Conservative NSW Liberal senator Concetta Fierravanti-Wells believes allowing a conscience vote on the issue would be perceived as a "cop out" and might lead to a disconnect between the Liberal Party's base and parliamentary wing.

"I do not believe there is at the grassroots of the Liberal Party any overwhelming support for a change to such a fundamental bedrock issue," Senator Fierravanti-Wells told the ABC.

She rejects suggestions from same-sex marriage advocates that change is inevitable, or even close, and expects more senior members of the Government to vocally "defend" the Coalition's official policy position.

"Whenever it comes up at whatever stage ... my sense is the view in the parliament will reflect the review of the majority of the Australian public," she said.

"That is marriage is between a man and a woman.

"There's only two things that are inevitable in life and that's death and taxes".

A number of Coalition MPs said they had been inundated with emails and letters from constituents urging them to oppose changes to marriage.

Some worry preference deals with minor parties, like Family First, could fall over if same-sex marriage is introduced.

In the lead-up to the last election, 72 per cent of people who identified as "right-leaning politically" opposed same-sex marriage, according to the ABC's Vote Compass survey.

Conservative members of the Coalition are pushing back against same-sex marriage, as more of their moderate colleagues come out in support of the idea.

Frydenberg defends right to advocate same-sex marriage

Assistant Treasurer Josh Frydenberg has defended his right to openly advocate same-sex marriage, after being criticised by some of his colleagues.

On the ABC's Q&A program Monday night, Mr Frydenberg said he believed there was enough support in the party room for a free vote on the issue and believed gay marriage would be legalised by the end of the year.

Assistant Treasurer Josh Frydenberg says he believes there is enough support in the party room for a free vote on gay marriage. ( AAP )

"I'm hoping there'll be a conscience vote in our partyroom," he said.

Those comments drew fire from ACT Liberal senator Zed Seselja, who said a number of Liberal supporters were concerned to see frontbenchers going against party policy.

"A political party not having a position on marriage would be very odd," Senator Seselja said.

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"So if people feel strongly enough about it, if they believe that there should be a change, they should move to change the party policy and they're free to do that.

"But we do have a very long-standing position on this, and I believe that the vast majority of our supporters support that."

South Australian Liberal senator Cory Bernardi said if frontbenchers wanted to vote in favour of same-sex marriage, they should resign from their positions.

"Somehow we've now got a circumstance where we've got frontbenchers who are prepared to undermine the current position and they get away with it," he said.

"It's quite extraordinary."

But Mr Frydenberg said the Prime Minister himself had previously acknowledged same-sex marriage was one issue on which MPs could disagree.

"We're not robots in this place, we all have a right to express our views and this is an issue where we need to respect the passionate views that are held on both sides of the debate," Mr Frydenberg said.

Opposition Leader Bill Shorten on Monday put a same-sex marriage bill to Parliament, while Coalition MP Warren Entsch is working on a cross-party bill and is hoping it will go to a vote by the end of the year.