Solidarity-PBP may seek a court injunction in an effort to progress the party's plan to change the rules of the Dáil.
The political grouping wants a debate on a motion that could end the stalling of 55 pieces of opposition legislation that have been rejected by Government.
These have been blocked using a mechanism called a Money Message.
This is where a Government can stop a bill from progressing if it impacts on the public finances.
However, Solidarity-PBP say many of the stalled pieces legislation do not meet this criteria.
Deputy Richard Boyd-Barrett described the situation as a savage attack on democracy and said court action may be necessary to ensure the debate goes ahead.
In the Dáil this afternoon, Solidarity-PBP TD Bríd Smith told the Ceann Comhairle that the Constitution allows her party to put forward motions to change the Dáil rules.
She said the Ceann Comhairle's ruling was unacceptable and she vowed not to be pushed around.
In response the Ceann Comhairle said the motion was not in order because it would allow legislation to progress through the Oireachtas in an unconstitutional manner.
Sean Ó Fearghail said that following legal advice he is satisfied this was the correct approach.
The Fianna Fáil Leader Micheál Martin accused the Government of not treating the Dáil with respect and of using the Money Message to block good legislation.
He stated that the best way to change the rules, the Standing Orders, was for political parties to work together.
However, Mr Martin added that he would not query the Ceann Comhairle's ruling.
The Sinn Féin Leader described what has unfolded as a very troubling set of circumstances.
Labour Leader Brendan Howlin said a mechanism must be found to resolve this impasse.
The Green Party Leader Eamon Ryan called on the Ceann Comhairle to share the legal advice he received on this issue.
Independent TD Thomas Pringle said the matter should go to the courts to get legal clarity.
Sean Ó Fearghail said that he would convene a meeting of the Dáil Reform Committee this evening to discuss the matter but he was not prepared to be bullied.
