The government has missed a self-imposed deadline to provide Labor a draft bill to set up a marriage equality plebiscite, shadow attorney general Mark Dreyfus has revealed.

Labor has stepped up its attack on the government for the failure to release details of the plebiscite, with equality spokeswoman Terri Butler warning the Coalition was running out of time to make its case for the popular vote.

Dreyfus told Guardian Australia the attorney general, George Brandis, “indicated to me last week a draft bill would be available by the end of the week, and none was forthcoming”.

Butler said if the government wanted to hold the plebiscite it should be “out persuading Labor the benefits outweigh the possible risks”.

She said the government had so far “failed to make the case” and was relying on the “mechanical” or political argument that a plebiscite is necessary because Malcolm Turnbull was not prepared to stand up to Cory Bernardi and the right wing of the Liberal party.

“I don’t think they’ve given it any thought beyond incorrectly claiming we can’t have marriage equality without a plebiscite.”

Dreyfus and Butler both called on the government to release the plebiscite-enabling bill.

“If they’ve got an argument [about why we should support it], they should make it soon,” Butler warned.

Labor is still heavily inclined to block the plebiscite. In August the opposition leader, Bill Shorten, warned he and his colleagues are on record opposing the plebiscite and said he is concerned Turnbull would “stuff up” the plebiscite.

The Greens and the Nick Xenophon Team have already said they will block plebiscite-enabling legislation, meaning, if Labor blocks it, the compulsory popular vote on same-sex marriage will not occur.

Dreyfus and Butler have released an eight-point list of Labor’s objections to the plebiscite, that: it would waste $160m; sets a bad precedent to have a popular vote in a representative democracy; the question could be doctored; it will provide a platform for hateful language; it singles out the LGBTI community by subjecting their rights to a popular vote; it will hurt vulnerable LGBTI people; it delays marriage equality; and is not binding on Coalition MPs.

Fairfax media has claimed a compromise could be reached with Labor if the plebiscite were self-executing, that is, a yes vote would automatically usher in marriage equality without a further vote in parliament.

But Butler said there were “many deal-breakers” with the plebiscite and the fact Coalition MPs can ignore its result “is just one of them”.

She said the plebiscite was a terrible idea and allowing the result to be enacted automatically merely “made a terrible idea more palatable”.

“We’ve made our opposition to the plebiscite very clear.”

Dreyfus said making the plebiscite self-executing was “an absolute minimum but would not be sufficient to get Labor’s support”.

“If there is a national opinion poll at the very least the government should make sure [same-sex marriage] doesn’t have to return to parliament, which could cause further delay or subversion of the will of the people,” he said.

On Thursday Liberal MP Trent Zimmerman told Sky News that it is “universally accepted that the outcome of the plebiscite should determine the fate of marriage equality”.

He said a majority of MPs would vote for same-sex marriage if the plebiscite agreed to it, so “the outcome will be reflected” regardless of whether the bill is self-executing or not.

“Once the cabinet has settled on a position, the government will have to talk to the Labor party and the crossbench in the Senate and, in the spirit of ensuring we have a plebiscite that succeeds, I would encourage the government to do so.”

On Thursday the Greens LGBTIQ spokeswoman, Janet Rice, called on Labor to “completely shut the door on a damaging, unnecessary plebiscite”.

“The Greens have listened to the LGBTIQ community, who have made it clear they don’t want a plebiscite under any circumstances,” she said.

A spokeswoman for Brandis told Guardian Australia the government had made “no promise” to provide the bill by the end of last week.

“The government, in good faith, has consulted with Labor and other parliamentary colleagues on this matter. The details of these consultations are confidential.

“The government committed to holding a plebiscite as soon as practicable and this was endorsed by the Australian people at the recent election.”