In the event Australia votes "Yes", the cross-party show of support gives Senator Smith's bill an edge over another proposal from Liberal Senator James Paterson, which would roll back anti-discrimination laws in order to strengthen religious and free speech protections.
"Certainly the government would not countenance making legal discrimination that is illegal, that is unlawful, today", he said.
Under Senator Paterson's plan, it would also allow any person or business to refuse to co-operate with the staging of same-sex weddings, protecting them from civil litigation under discrimination laws.
If the majority of Australians vote yes, and the ABC's survey is correct, then 70% of the House of Representatives and 68% of the Senate will vote for same-sex marriage.
Gay couples would be legally turned away from wedding service providers and anti-discrimination laws created to protect LGBT people overturned under an extraordinary rival same-sex marriage bill released on Monday.
"The people are being asked if we should treat LGBTI people equally".
"We will wait to see what the final bill looks like before we give a firm commitment as to how we will vote".
Brady, an Irish citizen, said he saw echoes of the historical discrimination against his own people in the religious freedoms push.
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The national director of Liberals and Nationals for Yes, Andrew Bragg, has said a marriage bill should be guided by three principles: "Firstly, existing discrimination in the Marriage Act should be eliminated; secondly, a strong protection for religious freedom should be provided; and thirdly, we should not reintroduce commercial discrimination in Australia".
No notice has yet been given for the Paterson bill.
There are many politicians who, like Zed Seselja and and Ian Macdonald, have expressed opposition to same-sex marriage in the past, but say they will vote in line with the results of the postal survey.
'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.
"You could potentially see a situation where a hire auto company could leave their customers stranded on the way to a marriage ceremony simply because the driver held a thought or belief against it". This is even if the belief had nothing to do with religion, ' Ms McLeod said.
Labor leader Bill Shorten said Australians expected the parliament to deal with marriage equality legislation before the end of the year.
Liberal Democrats senator David Leyonhjelm is in the process of drafting amendments to the Smith, many of which align with provisions in the Paterson bill.
TWO months ago, millions of survey forms were mailed to eligible Australian voters asking if they believed same-sex marriage should be legalised.