Federal Parliament could vote on same-sex marriage within weeks, but the issue could cause an eruption inside an already volatile Coalition.
MPs return from the winter break next week and some are determined to see the law changed quickly.
Some Coalition MPs believe the deadlock on same-sex marriage is overshadowing the rest of the Government's agenda.
They are discussing ways to deal with the marriage issue — arguing that ending the standoff would help the Government move on to other topics.
Federal Liberal MP Trevor Evans told the ABC a vote in Parliament would be the quickest and most efficient way to deal with the issue.
Mr Evans, who is gay, said he would raise the issue when the Coalition party room meets next week.
But that discussion is likely to provoke a fierce response from Coalition figures who oppose same-sex marriage or who believe the Government should stick to its pledge to have a plebiscite.
The bill for a plebiscite was defeated in the Senate last November and the Government has not tried to reintroduce it.
The plebiscite would be a non-binding national vote.
There is almost no chance it would pass the Senate if it was reintroduced, but some believe that another unsuccessful attempt would build momentum for a parliamentary vote.
Mr Evans is not ruling out crossing the floor to bring on a parliamentary vote on a private members bill being prepared by Liberal Dean Smith.
Liberal MPs have a 'right' to vote for same-sex marriage
Prime Minister Malcolm Turnbull acknowledged Mr Evans' right to exercise a conscience vote.
"In our party, backbenchers have always had the right to cross the floor," Mr Turnbull said on Monday.
"It's always been a fundamental principle in the Liberal Party and indeed the National Party. So it's a very different political culture to the very authoritarian and centrally controlled culture of the Labor Party."
Liberal politicians' open defiance of the Prime Minister and their party's election promise on marriage is making the party less attractive to values voters by the day.
Australian Christian Lobby managing director Lyle Shelton, who vehemently opposes same-sex marriage, described comments by Liberals who support it including Mr Evans, Trent Zimmerman, Warren Entsch, Tim Wilson, Senator Smith and Christopher Pyne as threats.
Mr Shelton insisted Liberals should stick to the promise to hold a plebiscite so that voters would have a say in deciding whether to change the law.
"Trust is the virtue a parliamentarian should cherish the most," Mr Shelton said.
"It is disappointing that so many Liberals do not seem to respect the people who elected them.
"This is making the party less attractive to the growing number of Australians who are concerned about the consequences of a change to the definition of marriage in law."
Conservative Liberal MP Craig Kelly has also warned any of his colleagues considering crossing the floor that the Government would suffer if they did so because they would be responsible for breaking an election commitment.
