The comments from Clonmel based County Councillor Michael Murphy come as a number of TDs within the party have put pressure on the Taoiseach to set out a timeline for his departure.
In a statement to RTE this morning FG backbencher Brendan Griffin said he believes only a change in leadership will avoid a general election in the autumn.
Meanwhile, the Health Minister says it wouldn't be desirable to have a timetable for when Enda Kenny will step down.
Senior government ministers have been defending the Taoiseach, saying any challenge to his leadership is a mistake.
Minister Simon Harris said the views of those TDs are 'premature' given that they voted for him as Taoiseach two months ago.
