The preference for moderate MPs is to use a private members' bill drafted by Liberal senator Dean Smith as a trigger for the Liberal party room to drop its election commitment to a plebiscite and allow a free vote in Parliament.

But there is a growing expectation in the Coalition that if this fails, moderate MPs fed up with the lack of progress will take advantage of the close numbers in the House of Representatives to bring on a vote on same-sex marriage.

In order to force a vote, three Coalition MPs would have to cross the floor and support a Labor motion to suspend standing orders.

Greens MP Adam Bandt, the Nick Xenophon Team's Rebekha Sharkie, Tasmanian independent Andrew Wilkie and Victorian independent Cathy McGowan would also have to support the motion. If that happened, Labor would then bring on Senator Smith's private members' bill.

Coalition sources said gay rights advocate Warren Entsch and gay MPs Trent Zimmerman, Tim Wilson and Trevor Evans were the most likely candidates to cross the floor to vote for it. The bill would be expected to pass the Senate, where the government does not have a majority.

Nationals MP George Christensen last month crossed the floor to support a Labor bill to stop cuts to penalty rates, setting a potential precedent for other MPs to do the same for issues important to them.

But MPs are acutely aware of the magnitude of defying party policy on such a totemic issue and the destabilising effect crossing the floor could have on the government. That is why a conscience vote is seen as by far the best way for the issue to be resolved.

Senator Smith on Monday said it was time for Parliament to "rise above petty politics" and deal with same-sex marriage.

"I just don't think the argument denying same-sex couples equality before the law can be substantiated any more," he told ABC Radio in Perth.

"And further to that I do think it is Parliament's job to decide the issue."

Prime Minister Malcolm Turnbull on the weekend said: "We support a plebiscite where all Australians will be given a vote on the matter.

"It is critical that all Australians be given a say and the only reason they haven't been given that say is because of Bill Shorten."

Senator Smith said Mr Turnbull was "100 per cent correct" to say it was government policy for a plebiscite to be held before any vote in Parliament.

But he said it was common for policy positions to change - such as on amending section 18C of the Racial Discrimination Act - thanks to advocacy by MPs.

"My view is the country is ready for a sensible pathway for same-sex marriage and importantly I don't think the plebiscite enjoys community support any more," he said.

"The plebiscite is a failed policy; it doesn't enjoy public support any more."

Senator Smith said he was finishing drafting his bill, which will include strong religious protections, and would present it to his colleagues so the issue can be resolved by the end of the year.

Mr Entsch said he was in "total agreement" with Senator Smith's stance.

"But I won't provide a running commentary on this, that would only stir up the crabs and make people agitated," he said.

Mr Entsch will travel to New York in September for a three-month secondment at the United Nations.

Liberal senator Eric Abetz, who opposes same-sex marriage, said: "The Prime Minister has made it very clear, yet again, that the Coalition policy is that of a plebiscite.

"We won the last election on that policy and I trust it will remain Coalition policy."