Leader of Government Business in the Lower House Michelle O'Byrne today made a final plea for the State Liberals to exercise their conscience when voting on Tasmania's historic same sex marriage Bill tomorrow.

Ms O'Byrne said this was a chance for the Liberals to be part of a momentous occasion in not just Tasmania's, but also Australia's, history.

"Tasmanian Gay and Lesbian Rights Group convenor Rodney Croome has stated publicly that there are Liberal MPs who agree with marriage equality.

"These Liberals need to stand up and vote with their conscience and not have their voices stifled by the draconian orders of the ultra-conservatives in the Liberal Party.

"Will Hodgman has shown he is too weak to stand up for a conscience vote, but that doesn't mean other Liberal MPs should not stand up for what they know is right.

"I call on the Liberals to exercise their conscience, and help deliver an outcome that Tasmania will be proud of," Ms O'Byrne said.