More than 60 amendments have been proposed by Fine Gael TDs and others seeking changes, including removing a section allowing abortion where a woman threatens to commit suicide.
However, the Cabinet is likely to sanction only a few changes.
European Affairs Minister Lucinda Creighton is prepared to lose her membership of the parliamentary party and her ministerial role and join other colleagues who have moved to the Independent benches.
Sources close to the Dublin TD say she and colleagues are sick of being “bullied” by Fine Gael leadership over the bill and of Labour’s agenda leading the way on the issue.
Fine Gael could lose even more parliamentary members this week if wavering TDs John Paul Phelan, James Bannon, John O’Mahony, and Michelle Mulherin vote against the bill.
Taoiseach Enda Kenny is thought to be anxious to keep Mr O’Mahony and Ms Mulherin onside, as both are in his Mayo constituency.
Others could go overboard when the bill begins its passage in the Seanad on Thursday.
Mr Kenny is known to have held private meetings with several anti-abortion TDs in recent days.
Health Minister James Reilly yesterday told RTÉ that changes were being made to the bill.
“There are a number of people who have been concerned that it wasn’t clear about the importance of protecting the life of the unborn and that has been made very clear now in amendments that are coming forward,” he said.
Meanwhile, a number of psychiatrists yesterday backed calls by Ms Creighton for a “care path” for women experiencing suicidal tendencies during pregnancy rather than having an abortion.