The federal government is at war with itself over the proposed same-sex marriage plebiscite, as two former cabinet ministers demand the Prime Minister Malcolm Turnbull hand over millions of dollars in taxpayer funding to both sides of the debate.

In a dramatic intervention, former defence minister Kevin Andrews backed church leaders, rather than the Prime Minister, in a dispute over whether Mr Turnbull promised taxpayer support to run the campaign against same-sex marriage.

The stoush comes as the Coalition's most long-standing supporter of same-sex marriage, Queensland MP Warren Entsch, called for Attorney-General George Brandis to be more transparent about the plebiscite process and work more closely with Labor.

Cabinet is set to debate the mechanism for the plebiscite on Monday before a party room debate on Tuesday.