Several senior Labour Party politicians are vying for contention in the leadership contest sparked by Tanaiste Eamon Gilmore's dramatic departure.
With all the names yet to be formally declared deputy leader and Social Protection Minister Joan Burton is the early favourite.
Another throwing his hat in the ring is junior minister Alan Kelly while Minister for Public Expenditure and Reform Brendan Howlin and junior health minister Alex White have yet to rule themselves out.
Declarations are expected to be known tomorrow before the lengthy election process takes place with about 5,000 party members eligible to vote for the new leader after the Dail terms ends for the summer.
July 4 has been pinpointed for the new regime to kick in and for talks on a likely cabinet reshuffle to begin.
Speculation mounted as the Government faced harsh attacks over their handling of reviews of the medical card system and Sinn Fein warning that the coalition learnt nothing from the devastating voter backlash.
Finance Minister Michael Noonan was forced to insist that ministers do not stand for the removal of medical cards from sick children, despite repeated controversies during the election campaign.
Days after taking a hit at the polls, Mr Noonan said the way the reviews were handled was being examined and changes would be introduced.
But he said only 5,433 people who were on the free health care scheme have been deemed ineligible over the last year.
Detailing figures, the minister said that out of a total of 77,925 discretionary medical cards in place before an eligibility review, 25,398 people continue to hold one on a discretionary basis and 37,906 have one on the basis of means.
About one fifth of the total no longer hold a card because of death, failure to complete the review and lack of response to correspondence from health chiefs.
Mr Noonan said the manner in which the medical card system was reviewed and revised will be examined by health ministers James Reilly and Mr White and changes introduced.
"Obviously it is a serious issue. The Government is committed to examining the situation again," he said.
"I would repeat that the Government does not agree with a policy of taking MC from sick children."
Mr Noonan said the wider medical card scheme entitles 42% of the population to free health care at a cost of about two billion euro to the state.
Micheal Martin, Fianna Fail leader, said discretionary medical cards have been taken from about 30,000 people over recent years.
"There's no question these were budgetary decisions to get savings in the Department of Health and when pressure came on the medical card system the ones that were focused on were discretionary," he said.
Sinn Fein president Gerry Adams said the coalition has learnt nothing from the elections.
"Friday's elections and the subsequent resignation of the Labour Party Leader, Eamon Gilmore, have contributed further to the destabilisation of a Government that is now in crisis," he said.