A brawl over gay marriage is looming in the Labor Party with a push to axe the conscience vote for MPs and senators.

It is one of several tricky issues facing Opposition Leader Bill Shorten in the lead up to July's National Conference, including whether the party will recognise Palestinian territories as a state and a battle over its stance on border protection.

Even more awkward is the move to overturn the conscience vote, which is being championed by his deputy, Tanya Plibersek.

In 2011, the party's platform was amended to reflect its support for changing the Marriage Act to include "all adult couples irrespective of sex".

But its national conference voted 208 to 184 to allow MPs and senators the right to opt out if it came to a vote in Parliament.

It was a close-run thing. Some delegates changed their position in order to ensure then-prime minister Julia Gillard was not embarrassed.

Get more stories like this Subscribe to get ABC News delivered to your email, including alerts on major breaking stories, daily wraps of the top issues and analysis and the latest stories on topics that interest you.

Ever since then there has been pressure to bind Caucus to vote in line with the platform.

Ms Plibersek has made no secret of the fact that she supports binding the vote, but would not comment on it yesterday.

"I'm on the record and have been for a long time as a supporter of marriage equality," Ms Plibersek said.

Push to overturn conscience vote worries supporters

The push to overturn the conscience vote even worries some supporters of marriage equality.

Shadow health minister Catherine King told Insiders she feared the move would harm the party.

"It is an area, to me, that does seem a bit odd. It's a bit of an anomaly that there is a conscience vote on this issue," she said.

"I support gay marriage and will vote for marriage equality if asked again within the Parliament, and I certainly think at some point we will have that in this country.

"But I also am a bit worried that this idea around not having a conscience vote might distract from the overall issue. It's potentially picking a fight we may not need to have."

The ABC has been told by a leading member of the right that the move was "stupid" because some of his colleagues would simply defy it.

Both Mr Shorten and Ms Gillard have criticised the Prime Minister for not allowing a conscience vote in the Liberal party.

In a strong defence of his support for gay marriage in a speech to the Australian Christian Lobby in October, Mr Shorten made it clear that he believed it was a matter of conscience.

"I believe in God and I believe in marriage equality under the civil law of the Commonwealth of Australia," Mr Shorten said.

"I know that many of you do not share my view — and I recognise that for some people of faith, this is a most vexed question.

"It is one of the reasons Labor has made marriage equality a conscience vote in previous parliaments, and today."