Appearing on ABC News Breakfast, Paterson confirmed key details of the bill and said he meant to protect the freedoms of the 30% to 40% of Australians who were likely to have voted against same-sex marriage.
Senator Smith's bill draws on the recommendations of a Senate committee and has the backing of the other prominent same-sex marriage supporters on the Coalition backbench: Trent Zimmerman, Trevor Evans, Warren Enstch and Tim Wilson.
The results of the same sex marriage survey will be announced at 10am AEDT tomorrow.
PM Turnbull has since expressed that his ministers will continue to back Smith's bill instead, although it will likely be adapted before being presented to parliament.
The ABC has pulled together a survey of literally every MP to find out how they'll vote on a same-sex marriage bill, and it's a handy way of finding out what your rep plans to do.
Sen. Dean Smith, a member of the ruling Liberal Party (which is actually conservative), drafted a bill with bipartisan support that would give religious officials the power to refuse to marry same-sex couples.
It would introduce "anti-detriment" provisions to shield government employees and licensed professionals from adverse action on the basis of the fact the person holds a belief that marriage is between a man and a woman.
"That's why it is necessary to extend the same principle applied in other same-sex marriage bills beyond ministers of religion to anyone else directly connected to a wedding".
But the opposition Labor Party, which backed Smith's bill, denounced Paterson's proposal as a "delaying tactic from the opponents to marriage equality".
"For those who want to see the marriage certificate, they're the ones waiting".
Senator Paterson believes state and federal anti-discrimination laws aren't strong enough.
The move has inflamed tensions between the conservatives and moderates in the party and set the stage for a lengthy parliamentary debate over religious freedoms and anti-discrimination laws. Cormann said thought the Smith bill was "a good starting position" but thought it would need improvement to "strengthen religious protections".
"It would be self-defeating to repeal discrimination and replace it with discrimination", he said.
If the "yes" vote does garner a majority, same-sex marriage could be legalised by the end of the year, with Turnbull previously saying he expected parliament to respect voters' wishes and act quickly.
"I don't believe Australians would welcome, and certainly the government would not countenance the making legal, discrimination that is unlawful today", Mr Turnbull told reporters on Tuesday in Manila, before heading home.
"This is just another attempt to delay passing marriage equality". "A yes vote can not and should not and must not become a moment where others try to unravel existing anti-discrimination law".