The survey results will be announced on Wednesday, but debate is intensifying on whether Australians who would refuse to provide gay weddings with a celebrant, venue, flowers or a cake should have added protection against anti-discrimination laws.
The Prime Minister Malcolm Turnbull has been grilled relentlessly by reporters over his leadership in the same-sex marriage debate.
While businesses would be able to boycott gay marriages, they would otherwise have to comply with existing anti-discrimination laws.
In remarks praised by his moderate Liberal allies as "strong", Mr Turnbull argued Australians would not support such moves - and neither would the Parliament.
Senator Smith said he was hopeful the Yes vote would prevail, but even if Australians voted No he would still introduce the Bill to the Senate this week.
"Australians are voting to make our country a fairer and more equal place, not to take us back to a time where people can be denied service at a shop", said Anna Brown, cochair of the Equality Campaign.
The Human Rights Law Centre said Paterson's bill was "a Trojan horse to allow unprecedented discrimination". "They won't be. constrained by any party policy".
The Equality Campaign has rejected the marriage equality bill put forward by Senator James Paterson as nothing more than a license to discriminate.
"There won't be a government position, there won't be a party position", Senator Cormann said.
"If you're a gay man or gay woman and you go into a florist and say, "I'd like to buy a bunch of flowers", it's just wrong and illegal for the florist to say, "I don't serve gay people" - just as it would be wrong or illegal for the florist to say to an Indigenous person, "I don't serve Indigenous people".
Government ministers instead backed the Smith bill, which legalises same-sex marriage while providing a moderate level of exemptions for religious organisations, and is backed by Labor, the Greens and others.
"Beginning the debate in the Senate allows the House of Representatives to debate the Bill in its last two sitting weeks of the year".
The Senator from Victoria said his bill would allow any Australian to declare that they would not participate in a same-sex wedding if it violated their religious beliefs.
If the result is Yes, Liberal and Labor MPs will have a free vote in Parliament.