A NSW Liberal MP has called on Tony Abbott to grant a conscience vote on same-sex marriage, saying the decision not to was allowing homophobia and hatred to build within the party.

Catherine Cusack was one of six Coalition members who supported a motion in the NSW upper house last week calling on the federal government to support same-sex marriage, which passed with support from the Greens and most Labor MLCs.

Taunted on Facebook ... the Liberal MP Catherine Cusack.

Following the vote, Ms Cusack received a number of angry emails and was subject to taunts on her Facebook page, with some comments coming from people stating they were members of her own party. She was accused of being a traitor and levelled with insults such as ''Shame on you. You are a stupid fat cow,'' and ''you are a sinner'' and a ''disgrace to our nation''. One commenter also referred to a gay MP as a ''poofter''.

Ms Cusack said that while her parliamentary colleagues had been very respectful of differences of opinion, she was shocked and disappointed by the ''homophobia from Liberal party members''.