For that reason, Labour, the Greens and other Opposition parties blocked a needless national plebiscite and the Government held a voluntary postal survey instead.
Now Australian Prime Minister Malcolm Turnbull is promising to act on the result by introducing legislation before Christmas. True leadership would not have needed this direction from the public.
Turnbull, long a supporter of marriage equality, disappointed liberal Australians when he retained the Coalition's policy for a plebiscite after taking the leadership from the conservative Tony Abbott two years ago.
Turnbull has been a disappointment on many fronts. He stands accused of the very fault he said he found in Abbott, a failure to sell a coherent economic strategy, and Turnbull is now two thirds of the way to losing as many successive polls as eventually sunk Abbott.
Nobody accused Abbott of lacking a coherent economic strategy but not many liked it. Turnbull, by contrast, has left Australians with a sense of aimless drift.
Without a clear guiding purpose in the Government, just about everything it has done has been received badly and every discordant note it plays becomes amplified in the echo chamber of political commentary.
To add to it all, the Coalition has lost the leader and deputy leader of its smaller National Party on the dual citizenship issue.
That may be bad luck rather than bad management, since the unseated MPs did not know they had mixed citizenship when they stood for election, but successful governments need some luck.
With the entire Australian Parliament now to be vetted for foreign-born parents, this crazy constitutional catch could yet bring down their Government. Former tennis professional John Alexander is the latest Coalition MP to be unseated by Section 44.
With the next Australian election not due until 2019, it is an open question whether Turnbull will survive as leader that long.
The economy is improving but even that seems not to be working in his favour. Now the same-sex marriage vote has given him the backing he needed to face down conservatives in his ranks.
The debates are not over - on the rights of objectors to withhold services to same-sex weddings, for example - but perhaps now Turnbull will find the strength to lead on these issues. Otherwise Australia could yet again see a mid-term change at the top.