Some Liberals have not ruled out crossing the floor to force the Lower House to debate same-sex marriage.
But others within the Coalition say that would be a dangerous move, because it would expose that the Government had lost control of the House.
Senator Abetz said they would be implementing Labor policy and abandoning the pledge the Coalition took to the last election.
He said that the Liberal Party had a very strong tradition of allowing people to cross the floor, but that he took issue with the idea they might vote to suspend other business to force the Parliament to deal with the issue.
“[It] would in effect set aside the Government’s agenda and the Government’s control on the floor of the House of Representatives,” Senator Abetz said.
“I think the Australian people would judge us extremely harshly if we had people within the Government that voted … to enable Labor/Green policy to be adopted in defiance of that which we took to the Australian people.”
The Prime Minister today refused to say how he will handle the next steps in the same-sex marriage issue that is threatening the stability of his Government.
Malcolm Turnbull insisted the Coalition’s policy is to have a plebiscite, which would give all Australians a vote on whether to change the marriage rules.
But the Senate blocked a bid to hold a plebiscite last November and Mr Turnbull has today refused to say if the Coalition will try again to pass that bill.
With the plebiscite blocked in the Upper House, some in the Coalition argue there should be a postal vote, which would not need legislation.
Mr Turnbull refused to take questions today on whether he supported that option.
Senator Abetz said he considered the postal ballot a second-best option, but argued it should happen if the Senate continued to block the plebiscite.
But he gave no guarantee that he or other members of Parliament would vote according to the result of any postal ballot.
“These postal ballots and a plebiscite are never actually binding — legally they cannot be binding” Senator Abetz said.