Taoiseach Enda Kenny could face a leadership challenge within a matter of weeks, several members of the party believe.
Mr Kenny’s leadership will not be the focus of the parliamentary party meeting this evening due to a Dáil debate on a confidence motion.
However, there is a growing acceptance the Taoiseach has lost the support of the middle ground in the party.
One Minister said Mr Kenny had served the party well but it had moved beyond his control.
“There is nobody feeling any joy on the back of this, but we have to accept that things are changing and an election could be called at any point.
“There is almost an acceptance that we are going to lose the next election. We need a new leader to re-energise the troops.”
Mr Kenny has come in for strong criticism from his party over his handling of the Garda controversy.
Carlow-Kilkenny TD John Paul Phelan has said there should be a new leader of Fine Gael within the next six to eight weeks.
However, leadership hopefuls Leo Varadkar and Simon Coveney have urged TDs to hold fire at present.
Mr Varadkar and Mr Coveney are the frontrunners to replace Mr Kenny, and many TDs privately believe they should approach the Taoiseach and ask him to set out a timeline for his departure.
A large number of Ministers and TDs believe it is up to both to go to Mr Kenny together and deliver such a message.
However, sources close to both Ministers, say that is extremely unlikely, and it is hoped Mr Kenny will step aside of his own accord soon.
Mr Varadkar and Mr Coveney have spent recent days attempting to calm members of the Fine Gael parliamentary party.
At least one TD said he wanted the leadership issue tackled this week, but the vast majority of the parliamentary party want to wait until the Sinn Féin motion of no confidence in the Government is defeated this week.
A number of TDs, beyond the usual hardcore group who are opposed to Mr Kenny’s leadership, have been pushing in recent days for a swift move against Mr Kenny.
