Two thirds of Australians want same-sex marriage legislated before year's end, according to the latest poll.
The federal government has bookmarked February 11, 2017 for its plebiscite on marriage equality.
"That is not very far away. It's months away," Prime Minister Malcolm Turnbull told reporters on Monday.
However, a ReachTEL poll of 2740 Aussies - commissioned by Australian Marriage Equality (AME) and Australians for Equality (A4E) - has found 65.7 per cent think it is either "somewhat important" or "very important" for parliament to legislate marriage before next year.
Almost half of those who answered "not at all important" were Liberal or National Party voters (46.9 per cent).
Labor is expected to formally reject the government's planned plebiscite when its caucus meets on Tuesday.
AME co-chair Alex Greenwich said the survey signals the majority of voters want immediate reform.
He said a blocked plebiscite would require "urgent action" from marriage equality supporters across the political divide to see the alternative of a free vote in parliament.
Australian Lawyers for Human Rights co-chair Nicholas Stewart said parliament should listen to the majority of Australians and "move on" with the vote, while A4E executive director Tiernan Brady said the government need only look overseas for advice.
"Just as Ireland, the USA, NZ, and the UK have put the unnecessarily divisive debate behind them, the Australian parliament has in its power to do this by the end of the year," Mr Brady said.
"Around the world we know once equality is embraced it is celebrated, and everyone moves forward."
The plebiscite versus vote debate has also raised concerns over the mental health impact on LGBTI people.
"There is a significant risk that individual's mental health will be impacted by the plebiscite and surrounding debate," Public Health Association of Australia chief executive Michael Moore said.
Australian Medical Association president Michael Gannon said he had no view on which method should be used to change the law, but that discrimination in the Marriage Act should end as soon as possible.
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