In the event of a "yes" vote in either case, the government would allow a private member's bill to legalise same-sex marriage to be introduced to the house in the final sitting fortnight of 2017.
Co-chair Alex Greenwich says the government's approach to marriage equality has gone "well beyond a joke".
Amid outrage from the Opposition and the LGBT community, Prime Minister Malcolm Turnbull sought to portray the postal vote as an attempt to keep a key election promise.
The government estimates the postal plebiscite would cost around $122 million - roughly $50 million less than the estimated cost of the full, in-person plebiscite.
One of Mr Abbott senior colleagues said the former prime minister should apply his own philosophy on the same sex marriage plebiscite to the RET and also the Paris climate change targets, which Mr Abbott agreed to as prime minister but now also wants to abandon. This is expected to be rejected by the Senate.
A postal vote would see ballots in voters' mailboxes in September, with an official result announced in November.
Whichever plebiscite happens, Parliament has two weeks to sit on the Marriage Act vote before potentially legalizing it.
Turnbull is insistent that he will let the voters have a say, "Strong leaders carry out their promises, weak leaders break them".
But Prime Minister Malcolm Turnbull said he was confident the postal ballot would survive any constitutional challenge.
" The Nationals have been staunch supporters of the plebiscite, with MP Andrew Broad warning the coalition could split if the policy was dumped. They will join talks on the mechanics of a potential postal vote in Canberra on Tuesday".
"We should have another go and if that fails, we should have another go", he said.
If the Senate again blocks the plebiscite, the government intends to hold a voluntary postal plebiscite by November 15.
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.
Responses would be voluntary and therefore less indicative of public opinion. Either way, the plebiscite legislation is likely to fail, given the staunch opposition from Labor, the Greens, Nick Xenophon and Derryn Hinch.
"The AEC also requires you to enrol at an address you've lived at for 30 days, so you need to be confident you have lived at a location for that time", he said.
"I believe that relationships, marriages should be available to people like (my wife and I), people of different sex and people of the same sex", Turnbull said.
"I find it extraordinary that those members of parliament putting forward this bill, who claim that religious freedom is central to it, have ignored the report preferring to have only a narrow number of exemptions for a small number of people", he said.
Lyle Shelton, managing director of the Australian Christian Lobby, said his advocacy group had collected 55,000 signatures on a petition demanding a plebiscite.
Ryan Goss, a senior lecturer in law at Australian National University, pointed to the internal politics of the conservative coalition led by the Liberal Party as a complication.
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