The prime minister is facing internal calls to solve the stand-off over same-sex marriage before the people next go to the polls.
Liberal MPs are urging Malcolm Turnbull to resolve the issue of same-sex marriage before the next election.
A number of MPs are expected to float options to bring the issue to a head at a Liberal partyroom meeting in Canberra next week - the first since parliament's long winter break.
"It's going to be the elephant in the room," one Liberal MP told AAP on Monday.
A growing number of MPs are pressing for a conscience vote on a private bill now that the parliamentary battle for a plebiscite has been lost.
Brisbane MP Trevor Evans, who is gay, says it has been six months since the plebiscite bill was defeated and it is time to consider a private member's bill.
"The issue now is in a stalemate and it's distracting away from the government's real achievements," he told Brisbane 4BC radio on Monday.
Mr Evans compared the situation to Labor's blocking of business tax cuts, which the government eventually negotiated with the Senate crossbench.
"When a reform is blocked, you try to find a new path."
Colleague Tim Wilson, who is also gay, argues Liberal MPs have discharged their responsibility to honour the party's election promise for a plebiscite.
"I have a personal conflict which torments, frankly, and challenges me on a daily basis and I'd like to see this issue resolved."
Liberal senator Dean Smith says the issue is putting lead in the party's saddle bags.
He has a private bill legalising same-sex marriage that he wants put on the Senate notice paper.
While the coalition agreement between the Liberals and Nationals has never been publicly released, it is understood to include a commitment to a plebiscite as the sole path to same-sex marriage.
Any breach of the deal is likely to seriously affect relations between the two parties.
One option being floated is to recommit the plebiscite bill to parliament, but make it clear that if the bill fails again, the government will hold a voluntary postal plebiscite.
The prime minister says coalition backbenchers have the right to cross the floor of parliament and vote against the government.
"It's always been a fundamental principle in the Liberal Party and indeed, the National Party," Mr Turnbull told reporters in Perth.
Conservative Liberal senator Eric Abetz told AAP the plebiscite is the "superior option" and effort should continue on trying to implement it.
"That said, in circumstances where Labor and the Greens are denying the Australian people a vote, it's worth exploring a postal plebiscite which wouldn't require legislation," he said.