Liberal senator Dean Smith, who has authored a bill which would legislate marriage equality, has asked Parliament to begin the debate on Thursday.
"The consensus position was the position that the Greens would support", he said, saying senators should "think very very carefully about entrenching discrimination to support your colleagues rather than this bill".
Results from the Australian postal survey on marriage equality are being announced today and senator Dean Smith is ready for a "yes" vote.
Mr Brandis said parliament would start the debate on same-sex marriage legalisation with Senator Smith's bill, if a "yes" vote is victorious.
'For example, the Bill would allow people to refuse to provide goods and services on the grounds of belief, thought and conscience taking us well beyond religious beliefs into unchartered waters.
In their contributions, the Labor leader in the Senate, Penny Wong, and the Greens leader, Richard Di Natale, warned that Australians had voted to "remove discrimination" from marriage law, not to add to it, signalling they are inclined to reject extending the right to conscientious objection to civil celebrants.
"I will now work constructively with my parliamentary colleagues over the coming weeks on amendments to ensure that the strongest possible protections for the freedoms of all Australians are enshrined in the final legislation".
In contrast, Smith's bill allows exemptions only for religious organizations and ministers.
"I believe that the Smith bill will need some improvements", he said.
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On the other side of the coin, the conservative bill backed by James Patterson - which was roundly slammed when its contents were released on Monday - doesn't look like it has much of a chance of getting up.
'The Smith Bill supports the protection of religious freedoms in two key ways.
Some 22 bills seeking same-sex marriage have been introduced into the federal parliament since 2004.
Throughout the day several Liberals who voted against same-sex marriage in the survey said they would vote in favour of it in parliament, including the assistant minister for cities, Angus Taylor, and the Liberal MP Lucy Wicks.
The Human Rights Law Centre said Paterson's bill was "a Trojan horse to allow unprecedented discrimination".
While Senator Paterson publically supports same-sex marriage, his bill had the support or a number of vocal No campaigners within the Coalition.
It is expected that same-sex marriage will be legalised following the plebiscite, and the LGBT community is seeking an anti-gay "loophole" to be closed.
They will attempt to table a string of amendments to the eventual marriage bill if their own proposal falls.
Various opinion polls point to a majority "yes" vote, possibly as high as 60 per cent.