Australia's first female Aboriginal MP Linda Burney says her son doesn't want a national vote to legitimise his same-sex relationship.
While her son wants to marry one day, Ms Burney says he doesn't want the law changed by a plebiscite.
The Labor MP also used the 1967 referendum that counted indigenous people in the population as an example of why a plebiscite would be damaging.
"When I was 10 years old this country had a referendum about my rights," she told parliament during debate on the plebiscite bill on Wednesday.
"I am lucky that I was mostly protected from the no campaign back then but there is no doubt that many were not.
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"Awful things were said about Aboriginal people."
That referendum had to occur, she added, because the change was made to the constitution.
A plebiscite was not needed for same-sex marriage, she said.
"This bill is an absolute failure of leadership," she said, adding it came from the "Neanderthal attitude of the right-wing rump of the Liberal Party."
Same-sex couples wanting to get married would prefer to wait until there was a free vote in parliament, she argued.
The Turnbull government's planned plebiscite appears doomed after the opposition formally rejected the bill.
The coalition hasn't won enough crossbench support in the Senate to get it through the parliament.
