The Australian government is set for a bruising encounter over same-sex marriage when parliament returns from its winter break this week, with government MPs threatening to break with official party policy and vote for legalisation.

The rightwing Liberal party’s one-seat majority could also be at risk with one MP threatening to quit the Liberal-National party Coalition if a parliamentary vote goes ahead.

The prime minister, Malcolm Turnbull, has called an emergency party meeting for Monday that is expected to bring the issue to a head as the idea of a postal plebiscite on marriage equality gains traction as a compromise between the Liberal’s two wings. The party will then have a meeting on Tuesday with its Coalition partner, the Nationals.

The Liberal senator Dean Smith released a private bill for same-sex marriage on Sunday as the parliament prepared to resume after a six-week winter break. He and five other Liberals have confirmed they would vote in favour of a marriage equality bill if it was presented to parliament.

Smith has called for the party to allow a free vote, just as former Liberal prime minister John Howard did when dealing with contentious issues including abortion drug RU486 and euthanasia.

Smith spoke out against marriage equality five years ago but changed his stance after the death of Tori Johnson in the Lindt cafe siege in 2014. Johnson, who was in a gay relationship, was shot in the head by Man Haron Monis.

“He and his partner had been wanting to get married or had been waiting to get married in the same way that so many gay and lesbian Australians are waiting to get married, and then his life was taken in such a tragic way,” Smith told the ABC.

If Smith puts forward the bill it will help the government MPs avoid being accused of crossing the floor, which could be the case if the opposition suspended standing orders to present its own bill.

The lower house Liberal MPs Tim Wilson, Jason Woods, Trent Zimmerman, Warren Entsch and Trevor Evans have all said they would vote in favour of marriage equality, which combined with crossbench and opposition votes would allow it to pass. It is expected a marriage equality bill would pass the Senate as well.

The government went to the 2016 election with a policy to hold a plebiscite on the issue but it was blocked in the Senate after marriage equality advocates campaigned against it. They claimed the campaign leading up to it would be damaging for LGBTI people and the vote would not be binding anyway.

Turnbull has maintained that the plebiscite is government policy but has left the door open to a postal plebiscite which would have people voluntarily voting on whether marriage equality should be legalised.

“Our proposition is there would be a free vote on same-sex marriage in the parliament if the Australian people approved of it in a plebiscite,” he said. “That was our policy.”

Turnbull argued against the prospect of a postal plebiscite during his leadership of the republican campaign in the 1990s, and supporters of marriage equality say it would be unfair on younger voters who are less likely to be enrolled, as well as on remote Indigenous communities.

The longtime marriage equality advocate Rodney Croome told Guardian Australia on Wednesday he was working with Parents and Friends of Lesbians and Gays to seek legal advice about the constitutionality of a postal vote, including whether the government could act without a specific budgetary appropriation.

“A postal vote would be unrepresentative of the voting population, nonbinding on politicians and have so little legitimacy it would resolve nothing,” Croome said.

“I’m particularly concerned that a voluntary postal vote would favour the no case because young voters, who are more likely to support marriage equality, are less likely to return their ballot papers.

“On top of this, the absence of enabling legislation means the government gets to set the question without any parliamentary oversight.”

Andrew Broad, a member of the National party, has previously said his support for the government is conditional on the plebiscite. If he resigned from the party the government would lose its one-seat majority, making it harder to pass legislation in the lower house.

The Queensland Liberal National party president, Gary Spence, sent an email to members criticising those who had supported marriage equality, saying he was disappointed views that do not accord with the party’s policy were being aired publicly.

“I am equally disappointed that members elected under the LNP banner have chosen to take a position that defies LNP policy and the wishes of the LNP’s membership,” he said.

Support for marriage equality is at an all-time high in Australia, with an Essential poll putting it at 62%. Last year 52% said they supported a free vote in the parliament if a plebiscite were blocked, and another poll found 54% of Christians supported marriage equality and 77% supported a parliamentary vote.

The immigration minister, Peter Dutton, has been touted by members of the right of the party as a replacement for Turnbull if there was a leadership spill and has called for members of his party to keep their views to themselves until the party-room meeting.

“My plea would be to people, it’s an emotional area, people have strong feelings on this topic and that’s obvious,” Dutton told 2GB radio.

The former prime minster Tony Abbott, who was leader when the plebiscite policy was conceived, has warned of “breaching faith” by holding a parliamentary vote. He has called for the plebiscite to be taken as policy to the next election despite previously saying it should only be policy for one term.

He declared Liberal MPs crossing the floor to trigger a parliamentary debate about marriage equality would reflect poorly on Turnbull, because it would be “a dramatic loss of discipline inside the government, a serious attack on the authority of the leadership”.

Labor has promised a free vote in the parliament in its first 100 days if it wins the next election.