After Labor introduced a bill in late May, Abbott - who personally opposes change - declared it an "important issue" that ought to be "owned by the Parliament and not by any particular party".
That was interpreted as sanctioning a multi-party approach, and as indicating a willingness to allow the Coalition party room to decide on a free vote. Currently, MPs and Senators are bound by the party's policy of conserving the status quo.
A conscience vote would enable frontbenchers such as Malcolm Turnbull to vote for change. And while most Liberals are opposed, it is believed that those in favour could combine with Labor and the Greens to get a bill narrowly passed.
Turnbull has said he expects same-sex marriage to be legal by the end of this year - a view echoed by Abbott's gay sister, Christine Forster. Right-wingers are pushing back against the sense of inevitability bolstered by Ireland's referendum and the US Supreme Court ruling.
Eric Abetz, the Government's Senate leader, warned yesterday that legalising same-sex marriage could "open a Pandora's box for all sorts of other potential possibilities", including polyamory - relationships between more than two people.
"Let's not be under any illusion that once you start unpicking the definition of marriage, there will be other consequences," he told Sky News.