"Don't underestimate the Australian people."

That was Dean Smith's message for his colleagues in the Federal Parliament at the beginning of debate over the bill expected to legalise same-sex marriage.

The Liberal senator's bill was introduced to the Senate yesterday after a majority of 61.6 per cent of Australians responded Yes to the national survey asking whether gay and lesbian people should be allowed to marry.

Today, he told his Senate colleagues the bill recognised the, "special place of marriage that transcends our civic and religious life" and how it would ensure LGBTI Australians would, "no longer be denied that blessing".

Citing a book passage, he spoke about how weddings were a day of celebration, where, "We see our parents' joyful tears and receive their blessing … when we hear our best friend's speech with love hidden in the humour … when the love of our life is admitted to our family, and we to theirs".

"Because of this bill, that blessing will no longer be denied to our LGBTI children," Senator Smith said.

Characterising the support demonstrated by the survey result, he said: "We saw a glimpse of the country that we all yearn for — a country that is fair-minded, generous and accepting.

"We saw a country that was willing to embrace its hopes rather than hold on to its fears."

Senator Smith's bill had cross-party support, from Labor, the Greens, crossbenchers and within his own party.

He paid special tribute to one of those Liberal colleagues — longtime same-sex marriage supporter Warren Entsch, who helped draft the bill.

"When I look at this victory and the thousands who made it possible, I keep thinking of one man: the one who carried the torch before there were any openly LGBTI members of the Coalition in the Parliament," he said.

"He has a wonderful mix of gruffness and empathy that made him the most unexpected but compelling warrior.

"This bill is more Warren's than anyone's — we simply walk in the tracks that he has laid."

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Senator Smith had a strong message for those seeking to make amendments to the same-sex marriage bill, arguing it was a fair bill that already sought to protect religious institutions.

"The postal survey was a vote on amending the Marriage Act. Full stop," he said.

"Let me be clear: amendments that seek to address other issues, or which seek to deny gay and lesbian Australians with the full rights, responsibilities and privileges that they already have, will be strenuously opposed.

"Nothing in this bill takes away an existing right, nor does any of it diminish an existing civil freedom."

He emphasised there were other worthy debates about freedom of expression and living out shared values that should be had in the Senate, but added: "They can live for another day."

"Australians did not vote for equality before the law so that equality before the law that has already been gained is stripped away," he said.

Dean Smith celebrated the Yes result yesterday with some of his colleagues at Parliament House. ( ABC News: Jed Cooper )

He acknowledged the "very genuine concerns" raised throughout the same-sex marriage debate by some members of the Christian faith and said he understood their fears about, "the change in Australian culture towards people of religious faith".

"I understand these fears — because they are reflections of the fears that LGBTI citizens have felt through our country's history. Fears about acceptance, fears about jobs, fears about hiding part of you, and yes, fears about violence," he said.

"This vote is not about — and must not be about — replacing one persecuted minority with another.

"Or giving one group hope, while inflicting another with fear.

"It must be about advancing the hopes and dreams of all citizens, no matter their sexuality, ethnicity or religion."

Senators lined up to embrace Senator Smith after his speech. ( ABC News: Jed Cooper )

His lasting message for his Senate colleagues, though, was to have faith in Australia's sense of fairness and decency and its willingness to be a country "for all of us":

"I never believed the day would come when my relationship would be judged by my country to be as meaningful and valued as any other. The Australian people have proven me wrong.

"To those who want and believe in change — and to those who seek to frustrate it — I simply say:

"Don't underestimate Australia. Don't underestimate the Australian people. Don't underestimate our country's sense of fairness, its sense of decency and its willingness to be a country 'for all of us'.

"Not only does our country live these values, it votes for them as well."