Supporters of same-sex marriage say a national vote on the issue would unfairly delay the law change.
Some coalition MPs and conservative senators such as independent John Madigan are urging a plebiscite on the issue after the 2016 election.
The push comes as Opposition Leader Bill Shorten announced at Labor's national conference at the weekend he would legislate for same-sex marriage within 100 days of government.
The party also agreed to bind MPs to vote for the Marriage Act change - rather than have a conscience vote - if laws had not been enacted by the end of the next term.
The national ballot would mean setting aside current talks on a cross-party bill, which could come to parliament as early as next month.
Social Services Minister Scott Morrison has previously spoken in favour of a plebiscite, which would be only the fourth ever held in Australia.
Mr Morrison's position is backed by a number of coalition MPs including George Christensen, Michael Sukkar and Kevin Hogan, as well as former Howard government minister Peter Reith.
Mr Shorten said Australians were sick of Prime Minister Tony Abbott looking for "distractions" to avoid giving his MPs a free vote on the issue.
"We don't need any more diversions, we don't want any more delays," Mr Shorten said in a statement on Tuesday.
Asked whether he'd been consulted on the idea of a plebiscite, Attorney-General George Brandis told reporters in Canberra on Tuesday: "The PM and I speak about a range of issues all the time."
Constitutional law expert George Williams told AAP a plebiscite would require the federal parliament to pass a bill allowing it to go ahead.
He said a national vote had been required in Ireland because of a constitutional blockage, but such a vote would not be needed in Australia.
"We normally should be cautious about national yes-no votes on people's basic rights and this will open up not only a lot of positive messages but negative messages, and that may do some harm," Prof Williams said.
Liberal frontbencher Christopher Pyne said it was right for the party room and parliament to properly consider the issue.
"The most likely way of bringing that about is not to try and bludgeon the parliament into debating it and voting on it, but dealing with it as appropriately and as carefully as possible," he said.
Opinion polls have shown 60-70 per cent of voters support allowing same-sex marriage - almost double that of a decade ago.
Senator Madigan, who opposes same-sex marriage, told AAP he would support a plebiscite.
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