There has been a call from a number of Fine Gael TDs to include a "sunset clause" in the planned legislation that will deal with the X case.
The proposal, first made in a letter to the Taoiseach by Cork North West deputy Michael Creed, would allow for the legislation on abortion to be reviewed after a number of years.
If it had led to an "opening of the floodgates" then the law could be looked at again, Mr Creed wrote in a letter released to RTÉ News under the Freedom of Information Act.
Labour TD Aodhan O Riordain has described the call from some in Fine Gael for a "sunset clause" to be included in the X Case Legislation as a "nonsense."
"You can't put a sunset clause on an Supreme Court constitutional requirement. It's a nonsense," he said.
The Dublin North Central TD branded some in Fine Gael and Fianna Fáil as being completely out of touch with public opinion.
"Talk of floodgates is incredibly irresponsible. This is cowardice from legislators whose responsibility is to protect women's lives and their constitutional rights," he added.
The call has been backed by Junior Minister Lucinda Creighton who said it was constructive and sensible and should be considered by Cabinet.
Cork South West TD Jim Daly said he met with the Taoiseach recently to urge him to accept this clause.
He added that it was a popular proposal and would ensure that abortion would not become widely available here.
Fine Gael TD for Mayo John O'Mahony also said he would welcome such a clause.
Minister for Communications Pat Rabbitte said he has no objection to the planned legislation being reviewed in a few years.
However, he said he did not believe a "sunset clause" was required.