Dean Smith says his bill shouldn't be seen as a vote on Malcolm Turnbull's leadership.
Same-sex marriage could be legislated by the end of the year, despite the government resubmitting its plebiscite bill to a likely lost vote in the parliament.
Liberal members attending a special meeting in Canberra on Monday stood by the policy taken to the 2016 election for a national vote on changing marriage laws.
However if the bill fails a second time - which appears likely unless the Nick Xenophon Team changes its position - a voluntary postal ballot would be conducted.
If the postal ballot comes back with a majority "yes", a private member's bill would go to parliament with Liberal members exercising a free vote on it.
The coalition joint party room meeting on Tuesday will discuss the timing of the next steps, but the compulsory plebiscite bill will be brought back to parliament this week.
Cabinet minister Mathias Cormann told reporters after the meeting the government's preference was for a compulsory plebiscite, but if they cannot get it through the Senate a voluntary postal vote would be held.
"The government is absolutely committed to keep faith with the commitment we made to the Australian people," he said.
He said the government had advice there was a "legal and constitutional" way forward on the postal vote, but the specifics were a matter for the joint party room.
It is understood only six people spoke in favour of a private member's bill at Monday's meeting and a letter from Brisbane MP Trevor Evans was read out in support.
Queensland Liberal MP Warren Entsch, who was among those pushing for a free vote, said the commitment to bring back the plebiscite this week was fantastic.
Mr Entsch says he reserves his right to take his own course of action on same-sex marriage but is quite happy to give a plebiscite a go.
"I'm not so much focused on the process. I want to get an outcome. And whatever it takes to get that outcome, I'm prepared to give it 100 per cent," he told the ABC's 7.30 program.
The Labor caucus was briefed on WA Liberal senator Dean Smith's private bill on Monday, agreeing that it represented an "acceptable compromise" and was in line with a Senate inquiry's findings.
Labor MPs would get a conscience vote on it if the bill came to parliament, which is possible if the compulsory or voluntary plebiscites pass.
Labor frontbencher Terri Butler said it was disappointing the Liberal Party continued to put up more obstacles to marriage equality.
"The Liberal Party is already aware the will of the parliament is not to have a plebiscite, because the plebiscite legislation has already been defeated," she told AAP.
"The Liberal Party in keeping with the sentiment of the electorate and the desire to do the right thing should seek to remove this discrimination against same-sex couples or at least seek to have a free vote on the floor of parliament, not recycle old ideas."
Speaking before the meeting, Senator Smith said a postal vote was useless.
"It's a D-grade response to what is a defining A-grade social issue," Senator Smith said.
Advocacy group Australian Marriage Equality has legal advice it says confirms a postal vote would be unconstitutional, warning of a High Court challenge to prevent it going ahead.
Co-chair Alex Greenwich attended Senator Cormann's press conference, telling reporters afterwards the government's approach to marriage equality had gone "well beyond a joke".
Mr Greenwich said the announcement sought to weaken the role of parliament.
"There will be disappointment felt from coast to coast tonight in Australia," he said.
"They had the opportunity to resolve this matter and they said no, they said we are going to drag this out."
The Nationals have been staunch supporters of the plebiscite, with MP Andrew Broad warning the coalition could split if the policy was dumped.
They will join talks on the mechanics of a potential postal vote in Canberra on Tuesday.