Fine Gael TD Alan Shatter has expressed concern that the Ceann Comhairle may be "making an each-way bet" by deciding not to resign until next week.
John O'Donoghue announced last night that he would stand down next week following months of controversy surrounding his expenses claims.
The Labour Party has welcomed the announcement, but Mr Shatter said today that Fine Gael had concerns that Mr O'Donoghue may be adopting a "wait-and-see" approach.
Mr Shatter says the Dáil could be dissolved if the Green Party conference this weekend fails to approve a new Programme for Government.
If this happens, Mr O'Donoghue would be automatically re-elected because of his position as Ceann Comhairle.