Tony Abbott's lesbian sister Christine Forster wants a plebiscite on same-sex marriage at the next election and not after.

Coalition MPs decided against a free vote on the matter following a marathon six-hour joint party room meeting in Canberra on Tuesday night, while prime minister opened to door to a referendum or plebiscite.

Christine Forster says if a plebiscite is what it takes, then it should be at the next election and not after.