An Oireachtas committee has been asked to examine the process around how Supreme Court Judge Seamus Woulfe was appointed.
While Justice Minister Helen McEntee has said she will come before the Dáil to take questions, opposition TDs are not satisfied.
Sinn Féin's justice spokesman Martin Kenny said: "Today I received an e-mail from the minister's office, saying that they proposed to come in on the 1st of December - that's next Tuesday week - that's the day that the restrictions are being lifted at 9.50 at night for her to take questions which are going to be scripted questions from the opposition where she can give scripted answers."
They want a full debate exclusively about the process leading to Justice Woulfe's appointment - with the Social Democrats writing to the Ceann Comhairle seeking that again.
Labour's Brendan Howlin has asked the Justice Committee to consider holding an inquiry into the process.
While his party leader Alan Kelly wants to know how happy the Greens and Fianna Fáil are with this way of appointing judges.
"Are the Green Party just there for the craic? Do they not take their role seriously?
"And Micheál Martin, I mean his position isn't credible - in fact, it's embarrassing, he's being treated like a fool".
While Seamus Woulfe himself is out of the political firing line, his appointment is causing no end of headaches for the Government.
On Thursday, Tánaiste Leo Varadkar defended Minister McEntee, saying she acted completely appropriately in appointing Mr Justice Woulfe to the Supreme Court.
The Government has been under pressure to explain why the former Attorney-General was promoted ahead of sitting judges with an interest in the job.
However it was confirmed on Tuesday that there was going to be no action against him over his attendance at the controversial 'Golfgate dinner' and the ensuing row within the judiciary.
A review by former Chief Justice Susan Denham found that he should not be forced to resign over the scandal - saying that would be unjust and disproportionate.
However, Chief Justice Frank Clarke had told Mr Justice Woulfe to step down.
Many TDs believe Mr Justice Woulfe's position is untenable - but that as he broke no laws there are no grounds for impeachment.
The focus has instead turned to his appointment, and whether Minister Helen McEntee ran a fair process.
Reporting by Sean Defoe