Backbencher Warren Entsch is reserving his right to cross the floor of parliament to vote against the government.
Advocacy group Australian Marriage Equality has legal advice it says confirms a postal vote would be unconstitutional and warned of a potential High Court challenge.
"Advice we received from [Ron Merkel QC] last week indicated the government can not act without specific legislation and a specific budgetary appropriation", said just.equal spokesperson Rodney Croome in a statement.
As Australia provides no legal recognition to same-sex couples, the pair's union was never recognised, and Mr Johnson's death certificate states that he was single.
Mr McLennan warned the process could further damage the ABS, which came under fire previous year for its handling of the national census and said he had heard "alarm bells" upon learning of the government's plans.
Cormann announced it would be the Australian Bureau of Statistics (ABS) rather than the Australian Electoral Commission that would run a postal vote.
The new tactic will be debated in a joint Liberal-National party meeting in Canberra today in a bid to give gay marriage proponents a new timeline.
"If that were to fail, the government believes that we have a legal and constitutional way forward that gives the Australian people a say on whether or not the definition of marriage should be changed".
A Bill to hold the compulsory plebiscite could be put to Parliament within a week but is unlikely to gain support in the Senate, or Upper House, where the ruling Liberal-National Coalition does not have a majority.
The postal plebiscite will cost an estimated $122 million, approximately $50 million less than a full, compulsory plebiscite, and $122 million more than a free vote in parliament. Voters could see the ballot as soon as September 12 and would have until November 7 to return their ballot.
After a two-hour discussion, only a handful of Liberal MPs, some sources say six, others say eight, raised their hands when Malcolm Turnbull asked people to indicate whether or not they wanted the plebiscite dumped now, and the party to move to a free vote.
"I'm a strong leader".
The conservative Liberal Party-led coalition was narrowly re-elected in July 2016 with a promise to let voters decide whether Australia should recognize same-sex marriage through a popular vote.
Senator Lambie said she held Mr Turnbull to account for failing to pass the original plebiscite, saying it showed "how poor" the government's negotiations with the crossbench had been.
"Every Australian will get to have a say", Turnbull told reporters in Canberra.
Sen. Cory Bernardi said he would vote against legalizing gay marriage no matter what the outcome of the vote, and Sen.
"Instead, they prefer to delay it with a goddammed plebiscite and/or postal vote that are not even legally binding", he wrote on Facebook.