A potential second bid to get the same-sex marriage plebiscite bill through parliament appears doomed.
Prime Minister Malcolm Turnbull is weighing up how to progress the issue, given the coalition promised at the 2016 election to hold a plebiscite but its enabling bill failed to clear parliament.
The vote in the Senate was lost 33-29, as Labor sided with the Greens, the Nick Xenophon Team and crossbencher Derryn Hinch to defeat it.
The coalition had on its side four One Nation senators, David Leyonhjelm from the Liberal Democrats and independent Jacqui Lambie.
Senator Xenophon told AAP on Tuesday his party - which has three senators and a lower house member -remained opposed to the bill, arguing it was a waste of taxpayers' money, the result could be ignored by the parliament and in any case MPs should decide on such matters through a free vote.
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The government needs 10 crossbench votes to pass bills.
If the plebiscite bill was to be reintroduced, it would likely have the four One Nation senators, the Australian Conservatives' Cory Bernardi, Senator Lambie and Senator Leyonhjelm on side, but still be three votes short.
South Australian independent Lucy Gichuhi could bring an extra number but it would not be enough.
Cabinet minister Mathias Cormann said the government had not given up on its plebiscite despite a fresh push by Liberal backbenchers for a free vote on a private member's bill.
Asked on ABC radio whether there was still a chance the Senate could pass the bill, Senator Cormann said: "Let's just wait and see. We went to the last election making a very clear promise we would give the Australian people a say and that is the policy position we remain committed to."
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The government was considering the next step.
"These are the matters the government is currently considering and there will be appropriate processes through the cabinet and through the party room to progress how we best can give effect to that (election promise)," Senator Cormann said.
News Corp Australia reported on Tuesday that unnamed right faction leaders were warning the prime minister's leadership would be "terminal" if MPs were given the green light to cross the floor.
Mr Turnbull said on Monday that coalition backbenchers had the right to vote against the government.
Senator Cormann, a key conservative, rejected the report, insisting Mr Turnbull enjoyed the support of cabinet and the party room.
Cormann dismissed reports Mr Turnbull could be replaced by Immigration Minister Peter Dutton if he allowed moderate MPs to break the government's election promise to hold a plebiscite on gay marriage.
Fellow frontbencher and conservative Zed Seselja also denied Mr Turnbull's leadership was under threat, lashing calls for a parliamentary vote on gay marriage.
"I haven't heard why we should be, one year after the election which we won, adopting Labor's policy," he told ABC radio.
A growing number of Liberal MPs are pressing for a conscience vote on a private bill proposed by Liberal backbencher Dean Smith.
The coalition joint party room will next meet on August 8, when parliament returns from the winter break.
