Deputy Labor leader Tanya Plibersek says the opposition could push Malcolm Turnbull to breaking point over action on same-sex marriage, even if it costs him the prime ministership.

With the government's planned legislation for a plebiscite on the issue set to be killed off in the Senate, Ms Plibersek said gay and lesbian families and advocates had told Labor they were prepared to wait in order to avoid a divisive public debate on the issue.

Tanya Plibersek urged Coalition MPs to back Malcolm Turnbull's own previous position of support for a free vote on gay marriage Credit:Andrew Meares

Ms Plibersek said Labor accepted the full moral and political consequences of the delay and called on Coalition MPs to back Mr Turnbull's own previous position of support for a free vote in Parliament on gay marriage.

The comments come as conservative backbenchers say they will abandon Mr Turnbull if he moves to allow a free vote, an apparent breach of the secret Liberal-Nationals Coalition agreement.