Prime Minister Malcolm Turnbull’s plan for a same-sex marriage plebiscite looks to have run its race, with Opposition Leader Bill Shorten signalling Labor will block it.

Mr Shorten says he fears a popular vote will fail and set back the cause.

“I’m worried Malcolm Turnbull will just stuff it up,” he said.

“He stuffed up the republic referendum, he stuffed up the NBN and he stuffed up senate reforms when he promised to fix it.”

Mr Shorten’s leadership group is believed to have discussed the issue behind closed doors last week and while no final decision was made, they appear likely to vote the plebiscite down.

Labor fears Mr Turnbull will put no effort into the “yes” campaign, allowing the well-organised and well-resourced “no” campaign to steal a march and ultimately carry the day.

Mr Shorten says a plebiscite on same-sex marriage is a “second-best option” but has not ruled it out, indicating he will need to see the details of the legislation before making a decision.

“We want to have marriage equality and we want to do it as quickly as possible. That’s why we think a vote in the parliament is the quickest, cheapest, least-divisive mechanism,” said the Opposition Leader.

“We haven’t seen Mr Turnbull’s plebiscite legislation, we’ll cross that bridge of what he intends to do when he presents that legislation. But in the meantime, I say to Malcolm Turnbull: stick with what you used to think, be true to yourself, and true to Australians.

“We need to see the detail,” he said. “What we need is the quickest, most fuss-free, least-controversial approach.”

Malcolm Turnbull has called for Mr Shorten to “disown” any indication Labor will block the same-sex marriage plebiscite or risk “absolutely destroying the credibility of his case” against a public vote on the issue.

The Prime Minister told Barrie Cassidy on the ABC’s Insiders program there were several arguments against holding a plebiscite on the issue, but the decision to potentially block the public vote would be “anti-democratic”.

“There are arguments to put against a plebiscite,” said Mr Turnbull. “You can say it costs too much money and so forth. The worst argument, the absolute worst argument against a plebiscite, is to say that it wouldn’t be passed. So if Labor is seriously saying that, they are saying, ‘Don’t consult the Australian people because they won’t give you the answer you want.’ It is the most anti-democratic argument.

“Bill Shorten, if his people have been briefing that last night, Bill Shorten should stand up today and disown that, otherwise he has absolutely destroyed the credibility of his case against the plebiscite,” said Mr Turnbull.

Asked whether the legislation was “doomed” if the plebiscite were to be blocked, Mr Turnbull was optimistic, saying he had “no doubt” it would be carried and the same-sex marriage bill will “sail through parliament”.

“I support it. I will be voting yes. So will Lucy,” he said.

Labor senator Sam Dastyari says he hasn’t given up hope a bill would pass through parliament to legislate same-sex marriage.

“We are not giving up on the idea that we can actually get the bill through this parliament and there may or may not be some conservatives who cross,” he said.

“The general premise that we can’t get passed with someone crossing the floor or can’t get passed this parliament, I don’t accept that yet … We are not giving up hope of getting something past.”

The senator for NSW was asked whether backing the plebiscite would be the lesser of two evils rather than to “leave gay couples with three more years of ambiguity”.

“That is the difficult choice and decision Bill Shorten and the Labor Party are deciding now,” he replied, adding that the party room as a whole will discuss the issue in the next week.

Christopher Pyne labelled Mr Shorten a “villain” who is taking the “political low road” for his decision to block the government’s proposed plebiscite on same-sex marriage.

“Bill Shorten will try to hide behind the pretence to stop a divisive national campaign … but the reality is Bill Shorten takes the political low road. He always has and he always will,” Mr Pyne told Sky News this morning.

“Bill Shorten and the Labor Party are saying they will not support a plebiscite, therefore putting at risk the possibility of marriage equality in Australia,” he said. “Mr Shorten cannot guarantee there will be a vote in the parliament on marriage equality … The only villain in the piece here is Bill Shorten”.

Mr Pyne said Mr Shorten’s motive to block the plebiscite was “purely political” and “hyperpartisan”.

“We have to deal with the very poor form of the Labor Party who profess to support marriage equality but that’s not how they act in the parliament,” he said.

Labor frontbencher Ed Husic told ABC Weekend Breakfast this morning many Labor MPs are of the view the government should “get on with the vote” and amend the Marriage Act through a parliamentary vote.

“I think there are a number of us, and I certainly am of the view, that we should get on with the vote, make the decision, do what the parliament is supposed to and provide for marriage equality,” he said.

“We’ve advocated for marriage equality. It’s seen a number of MPs over the course of the 12 months, myself included, saying we are prepared to support marriage equality and we should take this historic vote.”