A group of Government and opposition TDs hope to use the Constitution to bring the proposed abortion legislation to a referendum.
Under Article 27, the President can refuse to sign the Bill - if he is petitioned by at least 55 TDs and 30 Senators.
Members of Fine Gael, Labour and a number of Independents have held meetings in recent weeks to try to win enough support for the vote.
Among the deputies taking part is former Labour Party Chairman Colm Keaveney.
He said that the group does not want to leave the final say on the abortion legislation to the party whip system.
"This is a wonderful opportunity for deputies who are concerned about their conscience to cooperfasten whatever decisions they have to make,"he said.
"Whether that is under duress of a whip to have the support of the people with respect to that and it is not a divisive process
"The group together are both pro-life and pro-choice deputies who have a concern about the dernocratic deficit with respect to the deate on the abortion issue."
Update at 11.40am
The Transport Minister has said there is no need for a referendum on the new abortion legislation.