The Australian people have backed same-sex marriage in a postal survey with more than 12.7 million people voting and 61.6% saying “yes”.

An impressive 79.5% of eligible voters replied in one of the highest turnouts seen globally for a voluntary vote.

What happens next in Canberra’s febrile climate before people can start saying “I do” is the next hurdle for marriage equality supporters.

Six hours after the vote result was announced, a private member’s bill from Liberal senator Dean Smith which would legalise same-sex marriage — and includes religious exemptions — was introduced in the Senate.

It was drafted with support from Labor and some crossbenchers, most notably the Greens, so all sides of politics are generally happy with the compromise.

Here’s Smith introducing it:

Debate is expected to get underway tomorrow.

The bill is expected to pass through the Senate by next Thursday, November 23, then head to the lower house, which sits for a fortnight from November 27.

MPs in the major parties have been allowed a “free vote” on the issue, meaning they are not expected to align with their party, although both Labor and the Coalition are broadly in support of SSM.

Prime Minister Malcolm Turnbull flew back to Australia this morning after meeting with world leaders at the Asia-Pacific Economic Cooperation (APEC) conference in Vietnam, but even before his return is already trying to reign in the conservative wing of the government backbench, which is now scrambling to frame the agenda for same-sex marriage.

His first break today was rebel Liberal senator James Paterson withdrawing his rival bill, which allowed for business owners to put a sign in the window of their shop saying “I don’t serve gay weddings” based on “religious or conscientious belief”.

The Smith bill offers the right of religious organisations to decide who they marry, as well as letting them and religious schools teach their beliefs on marriage.

But introducing the bill today, Attorney-General and government leader in the Senate George Brandis said he planned to make two amendments.

Brandis wants to see further protections for people who did not want to be involved in same-sex marriages, extending the rights offering to religious ministers to civil marriage celebrants with a “conscientious objection” to same-sex marriage.

He 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” in order “to put the matter beyond doubt” for critics of SSM.

But Greens leader Richard Di Natale, a co-signatory to the Smith bill, said his party wouldn’t countenance any further changes because they’d already made “significant concessions” in putting together the existing draft legislation.

It sets the stage for what could be a difficult debate in the Senate over the next week and also offers a window for some opponents to attempt to delay passage of the bill, knowing that Parliament will rise for the long summer break in early December.

Conservative opponents of gay marriage have already used the debate as a surrogate in the Liberal party’s internal battle over Turnbull’s leadership, with arch-rival and former leader Tony Abbott spearheading the no campaign and today saying “I look forward to a parliamentary process that improves on the Dean Smith bill to implement same sex marriage with freedom of conscience for all, not just the churches”.

No advocates concede they’ve lost, but now they’re here to help improve things.

Today, following the result, Malcolm Turnbull made a plea for unity.

“I say to all Australians, whatever your views on this issue may be, we must respect the voice of the people,” he said.

“We asked them for their opinion and they have given it to us. It is unequivocal, it is overwhelming. They are our masters, we who were elected to Parliament. It is our job now to get on with it, get on with it and get this done, it’s fair.

“The people have voted ‘yes’ for marriage equality, now it’s our job to deliver it.”

Being able to deliver is vital to the Prime Minister starting 2018 still in the top job. It was a core promise at the last election.

And his political opponents know all too well the damage breaking a promise can do to a leader.

But hopefully, Turnbull will keep his word for the Australian same-sex couples who already have a wedding date set for this summer.

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