Sinn Féin will publish a motion of no confidence in the Government today.
The party is seeking support from Fianna Fáil and from opposition TDs for the vote, which will be held in the Dáil this week.
Sinn Féin Deputy Leader Mary Lou McDonald says people 'the length and breadth of Ireland' are outraged over the Government's handling of allegations against Garda Sergeant Maurice McCabe.
She says it is a 'kick for touch, cover up Government' that has lost its right to govern.
"I believe that they're playing games, I believe that they are being less than forthcoming in terms of what they know and what they knew as regards these matters.
"And most importantly of all, I don't believe that they have any appetite for really getting to the bottom of matters - or for bringing about the kind of reform that An Garda Síochána so deperatly needs".
However Fianna Fáil has confirmed it will abstain from voting on the motion of no confidence.
While the row between Fine Gael and Fianna Fáil deepened over when the Government found out about Tusla's role in the McCabe affair.
Leader Micheál Martin claims his party told the Tánaiste Frances Fitzgerald about Tusla's role on Wednesday, but Ms Fitzgerald insists she only learned about it in media reports on Thursday.
Both the Taoiseach Kenny and Justice Minister Frances Fitzgerald (pictured) have denied that the Children's Minister Katherine Zappone, gave them any information at Cabinet meetings, regarding the details of her meeting with garda whistleblower Maurice MCCabe and his family | Image: RollingNews.ie
The party's Dara Calleary says there are questions to answer and 'pulling the plug on the Government' will not solve anything.
"Look our position is that we want to get answers to this issue - collapsing the Government will not provide the answers that Maurice McCabe needs, will not provide the answers that the public need to have confidence in Tusla and have confidence in our policing system.
"Collapsing the Government at this stage also will not take anybody off a health waiting list, will not provide a house to anybody.
"Government, stable Government and an effective Dáil and Senate will do that".
Over the weekend, garda whistleblower Sergeant Maurice McCabe rejected an apology from the Health Service Executive (HSE) regarding false allegations of sexual abuse made against him.
It emerged earlier last week that that the child and family agency Tusla mistakenly created a file containing the false allegations as a result of a "clerical error."
On Saturday, the HSE released a statement confirming that the error was made by a staff member of the HSE’s National Counselling Service in 2013.
The HSE statement apologised "unreservedly to Mr. McCabe and his family for the distress caused on foot of this error” and said the executive would make arrangements to formally offer the apology to Mr McCabe, “as soon as possible."
It also claimed the HSE is, "satisfied that correct procedure was followed once this error was brought to the attention of the National Counselling Service."
It is understood the McCabe family contacted a Department of Health official to say the statement was "wrong."