The appeals process for any woman refused a termination after the initial assessment process was a source of conflict within the Coalition, which is due to put the issue to the Cabinet today, Government sources have indicated.

Health Minister James Reilly was said to be trying to find a last-minute compromise on that matter of contention.

Proposed heads of the bill to legislate for the X case are expected to say that a woman asking for a termination due to suicidal intent will be assessed by a perinatal psychologist after referral by her GP. Further assessment will then be made by two other experts, another psychologist and an obstetrician. At that point, a decision will be made on whether a termination can be performed.

The four key ministers tasked with bridging the gap between Labour and Fine Gael on the abortion issue, Dr Reilly, Children’s Minister Francis Fitzgerald, and the two Labour junior health ministers, Kathleen Lynch and Alex White, continued to hammer out the last outstanding point of contention on a “fair appeals process” as the clock ticked down to the Cabinet meeting.

The Fine Gael leadership is believed to be angry at an intervention into the X case debate by former taoiseach John Bruton, which one Fine Gael source branded “attention-seeking”.

However, Mr Bruton’s insistence that the suicidal element should not be included in the planned laws has emboldened rebels. The ex-taoiseach’s brother, Jobs Minister Richard Bruton, admitted Fine Gael found the issue “divisive” but denied the party was “tearing itself apart”.

Galway West TD Brian Walsh became the first Fine Gael politician to promise he will not vote for legislation that includes suicide as grounds for abortion.

The party machine moved to isolate Mr Walsh, with one senior figure saying the surprise move was due to the Galway TD “losing interest in politics”.

Other outspoken Fine Gael TDs concerned at the inclusion of suicidal intent in the Protection of Maternal Life Bill 2013, such as junior minister Lucinda Creighton, appeared to be holding fire until the proposed legislation goes for scrutiny before the Oireachtas health committee in the coming months ahead of a showdown Dáil vote in July.

Government chief whip Paul Kehoe called on TDs to wait and see the draft wording of the legislation and take part in debates on it before deciding.

Senior figures within both Coalition parties are believed to be unhappy with Dr Reilly’s handling of the X case legislation, with one source describing him as appearing “under-prepared” for last week’s Cabinet meeting, which saw tension erupt over the move in draft legislation to have six experts assess a woman citing suicidal intent.

Former Fianna Fáil minister Mary O’Rourke called for a much wider debate on abortion, specifically on whether it is still possible to give equal consideration to both the mother and the foetus in the Constitution.