Prime Minister Tony Abbott has committed to passing legislation legalising same-sex marriage if a national poll finds in favour of the issue, according to coalition backbencher Warren Entsch.

Mr Entsch's private members bill on the issue was briefly debated in Parliament today — but not in the House of Representatives.

The legislation was debated in the Federation Chamber, which takes the overflow of parliamentary business from the House.

The bill has cross-party support, seconded by Labor's Terri Butler, but its passage through Parliament is in the hands of the bill selection committee which allocates time for debate on private members business.

Mr Abbott is in favour of a plebiscite, or popular vote, on the matter.

A plebiscite would not be binding on the Government of the day, but Mr Entsch said he had received a guarantee from the Prime Minister he would act on its finding.

"It's already been committed by the Prime Minister that whatever that people's vote is, even though generally it is not binding to Government, we have made a commitment," he said.

"Whatever that vote is, we will legislate accordingly.

"[Tony Abbott] made that commitment, and this is why I'm quite happy to support it, whatever the decision of the people is, that is what will be locked in."

Meanwhile the Australia Electoral Commission estimated the cost of a plebiscite on same-sex marriage at nearly $160 million if held after the next election.

The Commission's submission to a Senate inquiry said that cost would be reduced to $44 million if the poll was held at the same time as the next general election.

Mr Entsch said the issue of cost was irrelevant.

"Cost, it's about democracy," he said.

"We could've saved a lot of that cost if we had a free vote, but a decision was made that we would take it to the people.

"And people have to accept [that] for them to have a right to express a vote, there is a cost associated with that.

"Whatever the cost is, there seems to be an overwhelming view that people want to have a vote on this."

Mr Entsch said momentum towards a vote was from both the groups in favour of same-sex marriage, and those against wanting to raise their opinion.