Minister for Justice Frances Fitzgerald has said that Fianna Fáil are aligning themselves with Sinn Féin, by considering a motion of no-confidence in the Ceann Comhairle.
Fianna Fáil says it believes Sean Barrett was lobbied by the legal firm representing the former Justice Minister Alan Shatter, for a debate to be cancelled.
Fianna Fáil has called on Mr Barrett to withdraw claims that the Opposition is trying to undermine him.
Sinn Féin says it has not yet decided whether to hold a motion of no confidence in Sean Barrett, while Fianna Fáil says it will discuss it at its next parliamentary party meeting.
Minister Frances Fitzgerald has said that Fianna Fáil could pursue alternative ways to get change.
"My first response is that Fianna Fáil are aligning themselves with Sinn Féin who have sought to obstruct parliament on numerous occasions," she said.
"So they want it both ways. It seems to me that if Fianna Fáil were serious about change in the Dáil, instead of walking out and standing on the plinth, as indeed Sinn Féin had done on a number of occasions, I would have thought that you'd go to the Committee on Procedure and Privileges, you decide how you want to see change in the Dáil."