Malcolm Turnbull sets date for $122 million marriage equality postal vote.

Australians will have their say on same-sex marriage by the end of November in a $122 million postal vote, if the Senate again rejects a compulsory plebiscite.

Liberal and Nationals MPs on Tuesday endorsed a plan to have the Australian Bureau of Statistics – which is still reeling from last year’s bungled census – conduct a postal ballot should, as expected, the plebiscite legislation fail to pass a second time.

Handing the job to the ABS and using ministerial powers would get around the need for legislation passing parliament and potentially head off a court challenge by marriage equality advocates.

Listen: Mia Freedman asked Prime Minister Malcolm Turnbull about same-sex marriage when she interviewed him for No Filter.

A similar approach was used by the Whitlam Labor government to choose a new national song.

If the plebiscite bill is unexpectedly passed, a $170 million compulsory vote would be held on November 25.

A postal vote would see ballot papers in mailboxes from September 12 and a result declared on November 15. But there would be no publicly funded “yes” and “no” campaigns.

Prime Minister Malcolm Turnbull said if there was a majority “yes” vote the government would bring to parliament in the final sitting fortnight of the year a private bill, on which Liberal members could cast a free vote.

If the vote came back “no”, no bill would go forward.

The coalition took its promise of a plebiscite to the 2016 election, with Labor arguing for Parliament to decide rather than waste taxpayers’ money.

“Strong leaders carry out their promises, weak leaders break them,” Mr Turnbull told reporters in Canberra on Tuesday.

“I’m a strong leader.”

Labor leader Bill Shorten asked the prime minister in question time on Tuesday whether he endorsed the “vile rubbish” of anti-gay-marriage campaigners such as former Tasmanian Liberal MP Chris Miles.

Mr Miles circulated a pamphlet last year which listed potential social outcomes of children of same-sex couples as sexual victimisation, sexual transmitted disease, drug use and abuse, depression and suicidal thoughts.

"Married biological parents ... minimise abuse and neglect of children," it read.

Mr Turnbull said the Coalition respected Australians' ability to have a "frank and forthright discussion" on the issue.

"But above all we respect them so much that ... we are doing everything we can to ensure that they have their say."

One of the Liberal members who rekindled the debate by drafting his own private bill, West Australian senator Dean Smith, said while he still believed a plebiscite would be "costly and divisive" he was pleased with the "clearer pathway" now in place.

Senator Smith's bill, which has Labor's backing, could be the legislation presented to the parliament later in the year.

"Extending marriage to same-sex couples and providing equality before the law will strengthen, not diminish, marriage in Australia," Senator Smith said.

Coalition backbencher Warren Entsch is reserving his right to cross the floor of Parliament to vote against the government if the plebiscite fails.