SYDNEY, Australia — Polls show broad public support for same-sex marriage. Politicians say they’re determined to let the people have their say. So why are so many Australians who want the law changed unhappy with plans for a national vote on it?

The government this week called for an extraordinary mail-in vote on whether gay and lesbian couples should be allowed to marry, and now Australians will have 14 days to register for ballots. The voluntary postal vote, which is being challenged in the High Court, went forward after the Senate rejected opening the polls for a mandatory, in-person one, as is normally required for Australian elections.

Many supporters of same-sex marriage deride the postal vote as a costly, “irregular and unscientific” gauge of public opinion. It would not itself change the law, and it would not be binding on lawmakers. Parliament would still need to approve legalization, and there is nothing legally preventing lawmakers from doing so whenever they wish.

Advocates for same-sex marriage accuse Parliament, which is dominated by the right-leaning Liberal Party, of ducking its responsibility, exposing gays and lesbians to a potentially bruising political campaign for no good reason, and all at a cost of 122 million Australian dollars ($96 million).