A bulging majority of Australians have declared their interest in the business of Parliament, and appetite is growing for giving the public another chance to have a say.

12.3 million people have returned their same-sex marriage postal survey forms, according to the latest update provided by the Australian Bureau of Statistics, representing 77 per cent of voters.

Barnaby Joyce yesterday called for an "omnibus" referendum in conjunction with the next federal election, covering multiple issues such as MP eligibility, constitutional recognition for Indigenous Australians and even the republic.

Outside constitutional matters, the high turnout to the same-sex marriage survey has rebuffed warnings Australians would be too lazy to fill in an optional survey or be unable to find a post box, and given weight to suggestions of a greater role for the public in Parliamentary business.

'Why wouldn't you have one on euthanasia?'

Dr Paul Kildea from the University of New South Wales said the Australian tradition was to leave our decisions to Federal Parliament outside constitutional reform, including decisions on difficult moral and social issues.

But he said there was merit to bringing the people in on certain issues and giving them a direct say.

"The Government has said we're going to hold a plebiscite on same-sex marriage but this should not set a precedent for other issues, when I think there needs to be some consistency and coherency about the position here," he said.

"It's more defensible for government to say, 'Look, there are socially contentious or moral issues that warrant a direct say rom the people — or perhaps there are issues that we as parliamentarians we feel we haven't been elected to decide upon — and on those issues we are going to hold plebiscites'."

ABC election analyst Antony Green said by having the same-sex marriage survey the Government exposed itself to questions about the next topic for such a poll.

"If you have one on same-sex marriage, why wouldn't you have one on euthanasia, it's got overwhelming public support," he said.

He noted one of the arguments against a non-binding poll was the lack of a formal mechanism for change if a vote was successful.

"One of the arguments against having the survey is exactly what is going to happen when this plebiscite is decided: the MPs are queuing up to delay it further or amend [the suggested bill]."

But he said community polls could help build momentum towards referenda, which would be more specific around changes.

How many Kiwi firefighters would you hire?

On Monday, shadow attorney-general Mark Dreyfus described referenda for the republic and constitutional recognition for Indigenous people as "more urgent" than one for clarifying MPs' eligibility.

Although the Federal Government has dismissed a constitutionally enshrined Indigenous advisory body, 61 per cent of Australians support it according to polling released on Monday.

Professor Graeme Orr from the University of Queensland said some issues were "gridlocked" in Parliament.

"We certainly need a circuit breaker on a lot of issues, but you can't have citizens' referenda on climate change, on economic issues — you're effectively trusting millions of individuated voters," he said.

New Zealand allowed citizenship-initiated referenda in 1993. These non-binding polls are triggered if 10 per cent of voters — approximately 350,000 people — sign a petition within 12 months.

Petitions on firefighter staffing, the size of Parliament, victim compensation, parents smacking and asset privatisation have met the threshold and went to a vote.

Only the two held during the election in 1999, on the size of Parliament and victim compensation, were successful.

"Abortion is still criminal in Queensland because the parties are too scared to upset the 30 per cent of people who are really strongly anti-abortion," Professor Orr said.

"There is a place for them, if you're going to deal with difficult issues.

"But be careful what you wish for, if you end up [with] government by lobby groups and corporations trying to get something on the agenda."