A New South Wales Liberal MP says she has received hate mail since voting in favour of same sex marriage, and that Tony Abbott's actions encourage an ugly tone to the debate.

Catherine Cusack was one of several Coalition MPs to support a motion which passed the state's Upper House last week, 22 votes to 16.

The motion, moved by Greens MP Cate Faehrmann, called on the Federal Government to change the Marriage Act.

Ms Cusack says since the vote she has been inundated with abuse via email and social media.

She says the debate in State Parliament was respectful, but much of the hate mail has been written by people who claim to be members of the Liberal Party.

State MPs from the Liberal and National parties were given a conscience vote on last week's motion.

Ms Cusack has taken aim at Mr Abbott for not doing the same in the Federal Parliament, saying the decision is allowing homophobia and divisions to build within the Liberal Party.

"Forcing us to vote against that puts members in great difficulty and it also seems to give permission for the more conservative members of the party to rip into the other half of the party," Ms Cusack said.

"I think the internal stability of the party is going to be undermined unless Mr Abbott allows a conscience vote.

"He's the Federal Leader and this is a matter for him and his federal colleagues, but I'm only really commenting on the experience that I have had in New South Wales and my concern for a breakdown of respect and the traditional way in which the Liberal Party has dealt with these issues.

"I don't believe for a minute that these views reflect Mr Abbott's, but it does tell me that by not allowing a conscience vote he's actually letting one half of the party completely rip into the other half.

"The glue bindings us together as Liberals is under threat."

On the other side of the NSW Parliament, Luke Foley was one of only two Labor MPs to vote against the gay marriage motion.

Mr Foley says he has since received thousands of emails on the issue, but most have been respectful.

"There's a few foul defamations, but a handful out of 5,000," he said.