Update 1pm: While a Commission of Investigation is to examine whether there was a smear campaign against Sergeant Maurice McCabe, the Government insists the Garda Commissioner has its full confidence.
However Cormac Lucey, former advisor in the Department of Justice, believes Noirín O'Sullivan needs to go.
"Here you're either all-in or you're not in, so either we have a Garda Commissioner there with full Government confidence or we don't.
"I think the question is why does the Government, or does the Government have full confidence in the Garda Commissioner right now - if I were in their position I wouldn't. I think the Gardaí right now are like the cat with nine lives, they're up to life 14 at this stage."
Earlier: Sinn Féin is to table a motion of no confidence in what it describes as a "kick for touch, cover up" government.
The move follows a week of pressure on the Government over hospital waiting lists and the latest revelations about an alleged smear campaign against Garda whistleblower Maurice McCabe.
Fianna Fáil's arrangement with the Government requires it not to support any motion of No Confidence, but Sinn Fein says it will encourage Fianna Fáil to support its move.
Sinn Féin Deputy Leader Mary Lou McDonald said the health crisis is a factor in tabling a motion of no confidence in the Government, but the situation involving Sergeant McCabe is of major concern.
"I suppose it is the turn of events around the scandalous campaign of vilification and character assassination against Sergeant Maurice McCabe, and the way in which the Government has failed to protect his interests and the interests of citizens more broadly in this very shocking scenario."
She said that the hospital waiting list scandal has "exposed the government's complete failure" in what she describes as a crisis in the health service.
Yesterday, Sinn Féin President Gerry Adams called for a General Election.
Speaking in Belfast on the controversy surrounding Sergeant Maurice McCabe, he said that the Fine Gael led government is '"stumbling from one crisis to another".
"They have covered up on the NAMA scandal and they are now playing the public for fools on the Garda/Tusla/McCabe controversy."
Mr Adams said that if his party was in government, they would not tolerate it.
He added: "People deserve an election. They deserve to have their say on all of these matters.
Also yesterday, the HSE said it is apologising unreservedly to Mr. McCabe and his family for the distress caused on foot of this error.
"The HSE is making arrangements to offer this apology formally to Mr. McCabe as soon as possible," the statement said.
The HSE said it will fully co-operate with any Inquiry or Investigation into this matter.
Sinn Féin is to use its Dáil time on Wednesday to table the motion of no confidence, with a vote the following day.