Same-sex couples will be able to marry legally from early in the new year, Attorney-General George Brandis predicts.
Parliamentary debate on a cross-party bill gets underway in the Senate on Thursday morning.
The upper house has cleared the decks of all other business until the bill wins final approval, likely by November 30.
Senator Brandis believes both the Senate and the House of Representatives can deal with the legislation before parliament is scheduled to rise for the long summer break on December 7.
He doesn't expect senators and MPs to get too hung up about the need for additional religious and conscientious objections protections than those outlined in the bill proposed by Liberal Dean Smith.
"The Australian people do not want us to now have a long, navel-gazing debate about religious freedom," the attorney general told Sky News.
Senator Brandis predicts the legislation, once it becomes law, will allow same-sex couples to marry from early in 2018.
Prime Minister Malcolm Turnbull has vowed to have parliament finalise same-sex marriage laws within weeks.
"It is a fascinating subject but I don't think anyone wants to be debating it on Christmas Eve so it will be done before Christmas," he told the Seven Network.
Conservatives are expected to propose amendments after an alternative bill, which sought to allow businesses that provide services to weddings the right to refuse service to gay couples on religious grounds, was abandoned.
Senator Brandis has already flagged two changes he will propose privately: extending exemptions for religious ministers to civil celebrants and ensuring people can legally have any view on same-sex marriage.
Senator Smith acknowledged millions of Australians voted 'no' in the voluntary postal survey.
"I see it as my task ... to reassure people that the sun will come up, as it did this morning, that there is nothing to fear from same-sex marriage in our country," he told ABC radio.
Senator Smith said he didn't want to see the strong vote to end discrimination against same-sex couples replaced with other forms of discrimination.
Conservative Liberal frontbencher Zed Seselja said the majority 'yes' vote wasn't a "blank cheque" for the Smith bill.
"I'm going to fight very hard for strong protections to freedom of speech and religion, and parental rights," he told Sky News, adding such principles were foundational to the Liberal and Nationals parties.
Labor frontbencher Jim Chalmers said it was crucial Mr Turnbull tell his MPs parliament couldn't afford more "dithering and delay".
"We haven't come this far to double back and retrace our steps on discrimination," he said.
"We've come this far to make Australia more inclusive, not less inclusive."
