Children are being exposed to hatred by the push for a public vote on same-sex marriage, Labor senator Penny Wong has told the Upper House.

"This ain't a respectful debate," she said in a passionate speech to the Senate this morning.

The Senate has refused to let the Government bring back the bill for a plebiscite on same-sex marriage, with Labor, the Greens and the Nick Xenophon Team combining to reject it.

The Government will now move to conduct a voluntary postal survey instead, although independent MP Andrew Wilkie and other same-sex marriage advocates have already launched a court challenge against it.

Senator Wong called the moves to ask Australians to vote a damaging and expensive stunt to avoid having Parliament decide on allowing same-sex marriage, and a sign of the Government's division and the Prime Minister's weakness.

A gay woman with two children, she was visibly angry about the tone of the debate.

"The Australian Christian Lobby described our children as the stolen generation," she said.

"We love our children and I object, as do every person who cares about children, and as do all those couples in this country, same-sex couples who have kids, to be told our children are a stolen generation.

"You talk about unifying moments? It is not a unifying moment. It is exposing our children to that kind of hatred."

She slammed Prime Minister Malcolm Turnbull for not intervening when those comments were made.

"I wouldn't mind so much if you were prepared to speak out on it. If the Prime Minister were prepared to stand up and say 'that is wrong'," she said.

Now that the Senate has refused the plebiscite again, the postal survey will be the next option.

The Australian Bureau of Statistics will run the process with ballot papers going to every enrolled Australian from next month, to be returned by November 7 and a result on November 25.

There will be a chance for Parliament to vote later this year, but there is no guarantee that will happen and MPs will not be bound by the result of the postal survey.

Mr Wilkie said the group had legal advice that the Government had exceeded its executive powers by bypassing Parliament.

"This is a democracy, this is a country governed by the rule of law," Mr Wilkie said, adding that it could even be illegal for the Australian Bureau of Statistics to run the ballot because it is only meant to gather statistics — not conduct ballots.

Editor's note August 12, 2017: An earlier version of this story said senator Derryn Hinch joined Labor, the Greens and the Nick Xenophon Team in voting against the move to bring back the bill for a plebiscite on same-sex marriage. Senator Hinch actually voted in favour of bringing the bill back before the Upper House.