The Turnbull government won’t reveal whether it has a same-sex marriage “Plan B” but is accusing Labor of driving a stake through the heart of the issue by killing off a proposed plebiscite.

The Labor caucus on Tuesday unanimously decided to vote down the enabling bill for a national vote in February 2017 even before debate gets underway in parliament.

Prime Minister Malcolm Turnbull said the opposition cared more about politics and less about people.

“The Labor party is not so much interested in same-sex couples being able to marry as they are in wringing every ounce of political gain out of this debate,” he told parliament.

Attorney-General George Brandis fired up in the Senate, saying the “cynical decision” meant debate would continue for years without resolve.

“The Labor party has driven a stake through the heart of marriage equality.”

But Mr Shorten said he could not in good conscience support the expensive and divisive plebiscite because of the “overwhelming” harm it would cause.

Instead Labor would continue to push for a free vote in parliament.

“I believe Malcolm Turnbull is capable of changing his mind,” he said.

The Australian Greens, also opposed to the public vote, are pleading for a compromise and urging both major parties to find a path forward.

Greens leader Richard Di Natale has written to both Mr Shorten and Mr Turnbull urging them to meet, while insisting same-sex marriage isn’t doomed.

“Tony Abbott’s divisive plebiscite is doomed,” he said.

“All three leaders of the main political parties support marriage equality, so let’s get this done.”

The Opposition criticised the plebiscite for months and its decision was widely expected. Photo: ABC

Same-sex marriage advocates are urging senators to block the plebiscite bill as soon as possible and get on with a parliamentary vote.

“The plebiscite needs to finally be killed off,” Australian Marriage Equality co-chair Alex Greenwich told Sky News.

While the government is adamant a plebiscite is the only way to achieve reform in this term, there’s hope Mr Turnbull could compromise.

The Prime Minister repeatedly refused to be drawn on whether there would be a free vote when questioned on Tuesday.

Such an outcome has already put some Coalition members offside: Nationals MP Andrew Broad has threatened to withdraw his support for the government if it went ahead with a free vote.

In the meantime, Senator Brandis is appealing to crossbenchers to change their mind on the plebiscite.

“It is not too late … to reconsider your position to give Australians the marriage equality you say they deserve,” he urged them.

-AAP