The Nick Xenophon Team, which supports marriage equality, said its three senators would not support legislation to authorise the plebiscite, which would effectively become a 160 million Australian dollar (£92.6m) opinion poll without legal weight.
Even if most Australians voted for same-sex marriage, conservative government lawmakers could still block the reform in Parliament, the party said.
Another party that favours gay marriage, the Greens, announced last week that it was also against holding the plebiscite. That leaves the opposition centre-left Labour Party as the government’s only hope of getting the Senate to back holding a popular vote on same-sex marriage.
Labour leader Bill Shorten supports marriage equality but has recently stepped up his attacks on the plebiscite plan.
Labour is waiting to see the proposed legislation for the vote before announcing whether its senators would back it.
“The quickest path to resolving this issue would be a vote in the parliament, and that’s what we will be seeking to do in the coming days and weeks,” Shorten said yesterday.
The Nick Xenophon Team and Greens agree with Labour that Parliament should decide without waiting for a non-binding popular vote.
“We should never put questions of human rights to an opinion poll,” Greens leader Richard di Natale said Friday.
Prime Minister Malcolm Turnbull agreed to hold the plebiscite in a deal with gay marriage opponents within his party.
In return, those opponents backed Turnbull in an internal leadership ballot that toppled Prime Minister Tony Abbott a year ago.
Turnbull, a gay marriage advocate, had previously spoken out against such a public vote that could create painful divisions in Australian society.
Gay marriage lobbyists are generally opposed to the plebiscite, which they argue was initiated by lawmakers who hope it fails.
Plebiscites and referendums – which are legally-binding popular votes – rarely manage to change the status quo in Australia.
Some marriage equality advocates warn that a lost plebiscite could likely set back their cause for decades.