Prime Minister Malcolm Turnbull's government introduced the bill after Australians overwhelmingly voted in support of same-sex marriage in a national vote.
On Monday, the debate on the Marriage Amendment (Definition and Religious Freedoms) Bill 2017 kicked off in the House of Representatives.
The bill has cleared both houses after passing the Senate last week and now only requires approval from the Governor General, a formality that will likely happen on Friday.
Under political pressure to find a solution, the ruling Liberal National Coalition government announced the non-compulsory survey in August, saying if the result was "yes" they would allow a free vote in Parliament.
"That is why I will support several amendments to the bill which will provide that additional reassurance in respect of their fundamental rights and freedoms", he added. And I said to LGBTIQ Australians in particular, you have given us a gift.
Abbott and other conservatives proposed amendments to the bill to include further religious protections, all of which were voted down. The major parties want the legislation passed this week after a majority of Australian's endorsed change in a postal ballot last month. "Equality isn't in our legal birthright of every Australian and this equality is long overdue", said Mr Shorten.
Some lawmakers, including former Prime Minister Tony Abbott sought to insert amendments into the Bill, but all of the proposed changes were voted down.
Many same-sex marriage supporters travelled to Canberra to witness the outcome in the lower house.
Fighting back tears, Liberal MP Sarah Henderson told the story Wednesday night of a close gay friend of hers who died months ago and who, in one of their last conversations, asked her to continue to push for same-sex marriage.
While marriage equality could become law this week, state marriage registries say they would not have the paperwork to proceed with weddings until January.
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