The Greens will vote against a bill to hold a plebiscite on whether Australia should adopt same-sex marriage and opposition leader Bill Shorten tweeted on Tuesday he intended to introduce a private member’s bill “to make marriage equality a reality”.

If the government’s plebiscite bill is passed, Australia will go to the polls to vote on whether the Marriage Act should be broadened to allow same-sex marriage, but critics of the plebiscite have complained about the estimated $160 million price tag on a vote that will be non-binding on members of parliament.

“They want to play politics but they may not ultimately get their wish to change the law,” Mr McCormack said.

“At the end of the day this is about giving every Australian a chance to have their say about whether marriage laws should change.”

Wagga Greens identity Ray Goodlass said it was just an “expensive opinion poll”.

“If it’s non-binding, why bother?” Mr Goodlass asked.

“Michael McCormack’s wrong, we don’t want to blow up anything, we think it’s an unneccesary waste of taxpayers’ money.”

Zoe Beaumont, from the Wagga branch of gay and lesbian group PFLAG, said the plebiscite would create a “toxic environment” for a vulnerable minority group.

“The only people who want to talk about this any more are hateful, it’s not the conversation we should be having,” she said.