The Coalition joint party room today endorsed a plan for a November 25 plebiscite if a bill to allow a compulsory vote is passed.
"Instead, they prefer to delay it with a goddammed plebiscite and/or postal vote that are not even legally binding", he wrote on Facebook.
Same-sex marriage is supported by 61 percent of Australians, a 2016 Gallup opinion poll showed, but the issue has fractured the government and damaged Turnbull's standing with voters.
That measure would make same-sex marriage legal by a national vote, while allowing religious leaders to refuse performing the rites to whoever they wish.
A postal vote, which the government believes can be established without legislation, would satisfy the election promise to consult the public before having parliamentary vote.
Activists have also labelled the postal vote a "bloody stupid idea" and vowed to launch a High Court challenge against any attempt to hold one.
Mr Sukkar told Sky News that MPs should be bound, whatever the outcome of such a vote.
"It's very disappointing that the Liberal Party has failed to do the right thing by the Australian people, but there is still a way forward", said Rodney Croome, a long-time advocate for marriage rights for same-sex couples in Australia.
Acting Special Minister of State Mathias Cormann bears responsibility for a popular vote.
"The government has a timetable that would facilitate resolution of this issue by the end of the year, but ultimately there are some factors that are outside of the government's control", he added, referring to the hostile senate.
Senator Cormann reiterated the government's belief, based on legal advice, that the postal option was legal and constitutional.
Mr Entsch said he was disappointed with the outcome of Monday's meeting and reserved the right to agitate for another free vote on same-sex marriage should the plebiscite return a no vote, potentially crossing the floor to side with Labor.
"Everyone Australian on the electoral roll will get a ballot paper and they will be able to fill that in and express their say", he said.
The 90-minute meeting heard from seven MPs and senators who pushed for a free vote.
The Equality Campaign's executive director, Tiernan Brady, said people should not lose sight that this was a debate about real Australians.
The government confirmed on Tuesday that the Australian Bureau of Statistics - you may remember them from such successful ventures as the #CensusFail - will be in charge of the votes. The government will aim to secure a final result by November 15, two months after ballots will be distributed.
PARTICIPATION in the ABS survey (previously known as "postal plebsicite") will be voluntary.
"Like it or not, Coalition MPs are honour-bound to oppose same-sex marriage in the absence of a plebiscite that's supported it; and we're equally bound to oppose any move to bring the matter into the parliament without a plebiscite first", he wrote.