The Minister for Health James Reilly has raised the prospect of extending the Dáil term to deal with the new abortion legislation.
Dr Reilly said he would rather see the Dáil sit for a few extra days before the summer recess, than put off the enactment of the new laws.
The Government has previously said the Bill would be dealt with before the end of July, but some TD's now say that would be "a big ask".
The Oireachtas Health Committee has now held three days of hearings into the Protection of Life During Pregnancy Bill.
The committee will report to the Minister for Health by the end of the month, leaving just a few short weeks for Dr Reilly to enact the controversial legislation before the Dáil finishes for the summer.
Chairman of the Oireachtas Health Committee, Fine Gael TD Jerry Buttimer admits that will be a difficult task.
Speaking in Dublin earlier, Minister Reilly said there is a real sense within Government that the issue should be dealt with before the summer break.
However, he said it is important that all sides in the debate get to air their views before the law is enacted.
Dr Reilly said: "Obviously we are going to be hard-pressed in terms of time, but I think we are on schedule and we will continue to work diligently to make it happen.
"The last thing we want is for anyone to feel that they don't have an opportunity to make a contribution so if the Dáil has to sit extra days, longer hours, so be it."