SYDNEY, Australia — The public opinion survey that yielded majority approval for same-sex marriage in Australia on Wednesday was an emotional breakthrough born of a long, curious and still-continuing struggle.

The survey drew a huge response, and the margin of victory sent a clear message about where Australians stand. But the costs of the mail-in survey — both financial and psychological — have been staggering.

So even as the “yes” side celebrates, many Australians are frustrated. Their country, they believe, could have gotten to this point faster if lawmakers and Prime Minister Malcolm Turnbull had simply done their jobs and passed a bill reflecting what previous polls showed most Australians wanted.

“I don’t feel like it says that we’re ahead of any sort of pack on this issue, but ultimately the popular will has overridden the cynical use of a system — and that’s heartening,” said Peter Lewis, one of Australia’s most respected pollsters for progressive causes. “It shows the people are way ahead of the current government.”