The debate on marriage equality is hitting taxpayers’ wallets as the government and churches tussle over whether millions should be forked out to fund campaigns during the plebiscite.

The prime minister, Malcolm Turnbull, is expected to reveal details of the planned plebiscite to his party room on Tuesday. He is likely to come under pressure from churches if those plans don’t include public funding for the “no” and “yes” cases.

Liberal senator Eric Abetz weighed into the debate on Monday morning, warning cabinet not to “steamroll” the coalition partyroom and deny taxpayer dollars for both sides in a plebiscite on the issue.

“This idea that you can have a proper plebiscite without funding for the yes and no cases would not be the sort of plebiscite that was envisaged by the partyroom,” he told ABC Radio.

One of the country’s most senior Anglican leaders, the archbishop of Sydney, Glenn Davies, said on Sunday that Turnbull promised him in February taxpayer money would be forthcoming, News Corp reported.

A month later, Davies reportedly met with the attorney general, George Brandis, who asked how much money would be appropriate.

Turnbull said he was not about to debate the contents of a private meeting and discussion.

“Any public funding, whatever the nature or terms may be, will be scrupulously equal as … between the ‘yes’ case and the ‘no’ case as you would expect,” Turnbull told reporters in Canberra on Sunday.



It could be more than $10m for each side, on top of the estimated $160m cost of running the national vote.

Senator Brandis said on Sunday there had been a very thorough process of consultation with all sides.

“What those stakeholders have been told on all occasions is that in arranging or designing the architecture of this plebiscite, both points of view ... will be treated by the government with strict equality,” he told reporters in Brisbane.

He acknowledged the plebiscite would be an expensive exercise and said the government was seeking to keep costs as low as possible.

The Australian Christian Lobby boss, Lyle Shelton, tweeted that he was at the February meeting and the archbishop’s recollection was correct.

“We can’t let foreign donations buy our vote, like Ireland’s,” Shelton wrote.

The Labor frontbencher Terri Butler said the latest debate showed the plebiscite plan was going from bad to worse.

Labor and lower-house crossbenchers will put separate bills legalising same-sex marriage to parliament on Monday and the latter group has written to the opposition leader, Bill Shorten, urging him to ditch Labor’s bill and get on board with theirs.

They say only legislation that is not “owned” by any one political party has a chance of attracting Liberal support.

Meanwhile, John Howard has defended opponents of same-sex marriage, saying it’s absurd to say their stance makes them homophobes.

“Sure there are homophobic people in our community, course there are, just as there are some racists,” the former prime minister told Sky News on Sunday. “[But] the implication from many on the progressive side of politics is that if you don’t support same-sex marriage you are a homophobe, that’s absurd.”

Howard’s government explicitly defined marriage in 2004 as being between a man and a woman.