Opposition TDs claim the Táiniste wants a two thirds majority lock on new abortion laws.
It would mean that if the 8th amendment is repealed after a referendum, the legislation could only be changed in future if two thirds of the Dail and Seanad votes for it.
The move is aimed at preventing the proposed laws from being liberalised any further.
It would mean no one political grouping could changing elements like the 12 week term limit on terminations without "specific indication."
Both the Iona Institute and Social Democrats TD Catherine Murphy have said the idea would be unconstitutional.
The constitution says that all votes in each house of the Oireachtas shall be determined by a simple majority of voters present, unless there's an article in the constitution saying otherwise.
Health Minister Simon Harris has said he's open to considering the idea.
