Neither bill has much of hope of passing because the government decides what gets on the parliament's agenda.

But former chief of staff to Tony Abbott, Peta Credlin has already explained how a vote on the parliament could be brought on by starting the bill in the senate.

It would then need three government MPs in the lower house to cross the floor to bring on a vote.

Prime minister Malcolm Turnbull still hopes to find a way to pass the plebiscite legislation and hold a non-binding national vote on marriage equality.