Sinn Féin launched its motion of no confidence in the Government over its handling of allegations against garda whistleblower Maurice McCabe.
Deputy leader Mary Lou McDonald said the Government is not capable of dealing with the issues around Sergeant McCabe and that an election was needed.
She also reiterated that she believed Tánaiste Frances Fitzgerald had misled the Dáil.
She said she was astonished to see the antics of Fianna Fáil, which she said beggared belief and questioned how they could maintain confidence in the Government.
Labour leader Brendan Howlin has said his party will be voting no confidence in the Government on Thursday.
For the Government to survive the motion, it will need Fianna Fáil to at least abstain in the no confidence motion.
Fianna Fáil justice spokesperson Jim O'Callaghan is challenging Ms Fitzgerald, saying he informed her of the Tusla file on Sgt McCabe last Wednesday, before RTÉ's Prime Time report on the controversy.
Ms Fitzgerald yesterday insisted she did not know about the referral of false claims to Tusla before the programme was broadcast.
Minister for Social Protection Leo Varadkar, who had been accompanying President Michael D Higgins on a State visit to Latin America, is to fly back to Ireland for the vote of no confidence.
Minister for Foreign Affairs Charlie Flanagan has said that after all the political manoeuvrings over the weekend, he believes it is important to step back and examine the objective of the Government and the Dáil - to ensure truth and justice for Sgt McCabe and anyone else involved.
Mr Flanagan said plunging the country into a general election would not help anyone involved, not least Sgt McCabe and others who appear to have been wronged.
He said it is his understanding that Mr Justice Peter Charleton is willing and ready to open the commission of investigation this week, adding that the first agenda at tomorrow's Cabinet meeting is the finalisation of the terms of reference.
The commission is to examine whether there was a smear campaign against Sgt McCabe orchestrated by senior gardaí.
Fianna Fáil spokesperson on public expenditure and reform Dara Calleary said that to vote the Government out this week would mean that the Charleton inquiry would not be properly resourced, and the focus of politics this week must be on justice for Sgt McCabe and to reassure people about the role of Tusla.
However, Mr Calleary said there are serious mis-communication issues at the heart of Government.
Speaking on RTÉ's Morning Ireland, he said that he cannot understand how Ms Fitzgerald failed to follow up with Minister for Children Katherine Zappone when she knew she had been due to meet Sgt McCabe.
He said failure to follow up was particularly surprising, given that Ms Fitzgerald was establishing the terms of reference for the Charleton inquiry.
Anything to do with a major breakdown by a State agency of a citizen's rights must be discussed at Cabinet, he added.
Call for Kenny to set out timeline on departure
Fine Gael TD for Dublin North West Noel Rock said that the country needs leadership and that the Government should issue a full and frank apology to Sgt McCabe.
Speaking on RTÉ's News at One, Mr Rock said the timing of Taoiseach Enda Kenny's departure as leader of Fine Gael is a matter for Mr Kenny.
However, he said that the Taoiseach should set out a timeline and that now would be a suitable time to do so.
He declined to say who he would support in a leadership contest.
Bruton defends Government's handling of issue
Minister for Education Richard Bruton has said the Government has handled the controversy in the best way.
Speaking on RTÉ's Today with Sean O'Rourke, Mr Bruton said when the Tusla matter came to Government, he believed Mr Justice Iarlaith O'Neill had set out terms of reference that were full and comprehensive and any issue regarding Tusla, or otherwise, would be fully investigated.
Mr Bruton said the core issue is that the way Government handled the matter was the absolutely correct way to do it.
He said he has absolute confidence that the terms of reference are in the public interest.
"We sought to ensure that by setting up an inquiry we did not cast aspersions on anyone until that evidence was sifted and, I think, that was what we wanted to do.
"Of course, the Dáil has now additional material, which is in the public domain, and that has been ventilated, but the terms of reference will be comprehensive."
Meanwhile, Chair of the Joint Oireachtas Committee on Children & Youth Affairs Jim Daly has said he thinks the terms of reference of the Charleton inquiry should now be expanded to include the information in relation to Tusla.
Speaking on Morning Ireland, the Fine Gael TD said he finds it "incredulous that a clerical error could be attributed to such a massive, massive, grotesque mistake, where such serious allegations could be transferred from one file to another".
The CEO of Tusla has been invited to appear before the next session of the committee on 22 February.
Social Democrats table motion for public inquiry
The Social Democrats have table a Dáil motion calling for a public inquiry into the McCabe affair.
Co-leader Roisin Shortall said the motion will be brought to the Dáil Business Committee tomorrow.
They are also calling for the Garda Commissioner to stand aside for the duration of the inquiry and be replaced by an international police officer, in a caretaker capacity, for that period.