Nóirín O’Sullivan’s future as Garda Commissioner will depend on her supplying a comprehensive statement within the next 48 hours giving a detailed explanation of how the latest scandals affecting the force arose.
The issue will dominate Tuesday’s Cabinet meeting.
It is also likely Ms O'Sullivan will be called to appear before the Oireachtas Justice and Equality Committee on Wednesday to face questions on the matter.
Time will also be set aside to allow the Opposition question Minister for Justice Frances Fitzgerald about her department's state of knowledge.
However, she has expressed confidence in Ms O’Sullivan since the unprecedented revelations last week that a million breath tests recorded by Garda members across the country had never taken place.
There are deep concerns in political circles that no explanation has been offered and the crisis is closing in around Ms O’Sullivan.
An audit into the discrepancies in the figures began in August 2015, some 13 months after the Medical Bureau of Road Safety first flagged the inflated figures.
The existence of the audit was not disclosed to the Policing Authority, with members learning it was under way via a report in The Irish Times. This is despite the authority and the Garda holding ongoing private meetings on the issue of road safety.
Members of the authority were also shocked at the scale of the inflating of breath-test figures. The two million tests were recorded by the Garda between 2012 and 2016 when only a million were carried out.
Ms O’Sullivan issued a statement on Saturday saying the problems were unacceptable, but she did not address what for many are key issues.
Fianna Fáil, which holds the balance of power in the Oireachtas, laid down an ultimatum to the commissioner on Sunday.
The largest Opposition party said it could not express confidence in Ms O’Sullivan unless she clarified how the Garda wrongfully prosecuted thousands of traffic cases. It said her statement on the breath-testing controversy was inadequate.
Fianna Fáil and the Greens both said over the weekend they no longer had confidence in the commissioner in light of the latest revelations, while Independent Alliance Minister John Halligan has also expressed deep unease.
On Sunday, Fianna Fáil leader Micheál Martin made his party’s confidence in the commissioner contingent on her making a detailed statement on the scandals, and also alerting the public to other unstated “bad practices” she referred to in her statement.
"The bottom line here is we can no longer articulate confidence in the Garda Commissioner, or indeed at this particular point of time, in the administration of justice, unless we get absolute clarity in plain language as to what happened here," he told RTÉ.
Taoiseach Enda Kenny and Minister for Social Protection Leo Varadkar both expressed confidence in Ms O'Sullivan, while agreeing the practices were "unacceptable".
“They are appalling and it is important there is accountability,” said Mr Varadkar. “The Government’s view though is that the commissioner is part of the solution and she has put in place the two solutions to these problems in the past couple of months.”
Sinn Féin said it would on Monday publish a motion of no confidence in Ms O’Sullivan.