The poll, carried out by Amarach consultants, found 78% believed politicians should be able to vote according to their own beliefs compared to just 13% who said they should vote along party lines.
Pro Life Campaign spokeswoman Caroline Simons said this view was also held by “many” in Fine Gael but they were coming under extreme pressure to toe the line.
“Several Fine Gael TDs we have spoken to in recent days are very upset and even distressed at the way they are being pressured to vote for the bill,” she said.
The poll of just under 1,000 people also found a majority oppose allowing abortion for suicidal women without strong medical evidence that it is a suitable response in such cases.
Those questioned were asked for their views on abortion “if it were clearly shown that abortion is not a suitable treatment for a pregnant woman with suicidal feelings”.
About 60% said they would be unlikely to support abortion on such grounds while 40% said they would be likely to do so.
Ms Simons said previous polls giving a contrary result did not draw attention to the lack of medical evidence for abortion as a response to suicidal feeling.
“The Government is aware from two Oireachtas hearings that there is no medical evidence abortion is an appropriate response to a suicide threat but they have refused to present this reality to the public.”
The poll also found a 69% to 31% majority for prohibiting abortion while allowing all necessary lifesaving treatment for women.
“These polls differ from other recent polls by clarifying the important distinction between ethical lifesaving treatment and induced abortion including on the suicide ground where the baby’s life is targeted.
“The Government should stop misrepresenting the situation, listen to experts and respect the informed opinion of the Irish people.”