"I support there being strong religious protections in the bill, should tomorrow the Australian people have decided through the marriage survey that they would like to see same-sex marriage legislated in Australia", he said.
Senator Smith is aiming to introduce his bill to the upper house on Thursday.
Should the survey return a "yes" vote, the Australian government are expected to debate a number of proposed exemptions to the law.
"After a cost of $122 million, and over two months of campaigning and years of public discussion, it makes no sense to delay a parliamentary debate".
According to a report in the Australian the bill would override state and territory anti-discrimination laws to allow refusal of same-sex weddings by anyone who holds a "conscientious belief" in traditional marriage, in effect allowing discrimination by private service providers even where they lack a contrary religious belief.
'While the Law Council does not endorse every detail of the Smith Bill it represents a better balance from a human rights perspective and represents greater fairness, including those affected by winding back anti-discrimination laws, ' Ms McLeod said.
"After the result is known on Wednesday, it is my intention to canvass support to introduce a Bill this week".
"In our eyes, Nicole and I are already married", she said. Any amendments to the bill will be reserved for that sitting week.
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This gives the Smith bill an immediate advantage over its legislative rival, a bill penned by Liberal senator James Paterson.
"Like millions of other Australians, I will be disappointed if there is a No result, but I will uphold my original commitment and present my Bill to the Senate without any expectation it will be debated", he said.
On Sunday the Liberal MP Trent Zimmerman warned that religious freedom was a separate issue to same-sex marriage. The legislation allows clergy and religious organisations to refuse to marry gay couples.
Senator Paterson said he was a supporter of same sex marriage but also believed there was a need for religious freedoms to be protected. But then after the marriage ceremony, the Bill remains silent on what happens if, say, a school teaches that marriage is between a man and a woman. If passed, this law would, for example, allow a baker to refuse to bake a cake for a gay couple, or students to "opt out of classes that conflict with their values", said Paterson.
Opposition Leader Bill Shorten said Labor would give the Smith bill "very favourable consideration".
Turnbull has endorsed a bill that would allow churches to refuse to officiate same-sex marriages.
"They can be debated ... but they shouldn't be confused with this bill which is created to deliver marriage equality".