But the Liberal senator David Fawcett, who chaired the Senate committee inquiry into same-sex marriage from which Smith's bill was drafted, told Guardian Australia the inquiry had concluded that religious freedom needed to be positively protected.
Senator Paterson, who voted yes in the marriage postal survey, says any ensuing law changes shouldn't have negative consequences for opponents of same-sex marriage.
A rival bill from Liberal senator James Patterson was withdrawn, with the Victorian saying a majority of senators believe the Smith bill "is where we should start".
And "to put the matter beyond doubt", Brandis also wants to add an amendment "that nothing in the bill makes it unlawful for people to hold and to express the views of their own religion on the subject of marriage".
It is a joint bill with Liberal colleagues Linda Reynolds and Jane Hume, Labor's leader in the Senate Penny Wong and her colleague Louise Pratt, Greens leader Richard Di Natale and his colleague Janet Rice, as well as crossbenchers Skye Kakoschke-Moore and Derryn Hinch. "Personally, I believe that the Paterson bill goes somewhat too far".
Senator Smith is aiming to introduce his bill to the upper house on Thursday.
"I would like to think that the parliament will be able to meet somewhere in between to give effect to the decision of the Australian people ... and to also ensure that we accommodate the legitimate concern of many Australians for there to be appropriate levels of religious protections".
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He also told how they were paid for their votes on the executive committee for choosing hosts of the World Cup. Fox Sports did not immediately respond to requests for comment on the testimony, multiple outlets reported.
"If there is a Yes result on Wednesday, Australians will have voted for true equality for all Australians - not an unfettered right to discriminate for people who voted No", said HRLC director of legal advocacy, Anna Brown.
While Senator Paterson publically supports same-sex marriage, his bill had the support or a number of vocal No campaigners within the Coalition.
It permits ministers of religion and religious marriage celebrants to refuse to solemnise a marriage and it allows bodies established for religious purposes to refuse to provide goods or services for the purposes of the solemnisation of a marriage, ' Ms McLeod said. This Bill will encroach on many of these protections in an extraordinary and perilous way'.
'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.
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.
64% of those who voted backed Yes, according to a Guardian Australia poll, up 4% from similar polls in recent weeks.
One Nation, which controls three votes in the Senate, has reserved its position.
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