As Sinn Fein and independents celebrate taking 45 percent of the vote in the European and local elections, the coalition parties have vowed to take action.
Labour has been wiped out at Europe and at home while Fine Gael has seen its general election support of 33 percent cut by a third.
Gilmore is under the most pressure with a handful of young Labour Party deputies openly calling for his head after the election slump.
Clare deputy Michael McNamara said: “The entire front bench of the Labour Party has failed and needs to go en masse, with the exception of Brendan Howlin.
“The party’s ministers are tired, bereft, out of ideas and out of touch with the generation that voted for us.
“If Labour is to continue in office we should do it on our terms and not just implement Fine Gael’s manifesto.”
McNamara is to raise Gilmore’s leadership at a Labour Party parliamentary meeting on Wednesday, while Kenny and his deputy will discuss the crisis on Monday afternoon.
Kenny has told reporters that he understands people are hurting, but warned there is no pot of gold to cure the country’s economic ills and remove the need for austerity.
The Irish PM said: “The situation that has been put in place by the people is a stark reminder of frustration, impatience and anger and a wearing out process. We have been very clear with the people that there is no pot of gold.
“We have been listening, but we’re not by any means perfect. At the end of the day what the Government have to do is look after those who are vulnerable to the best extent possible.
“What we want to do is take away the fear and anxiety of what people have about losing the medical cards. We live in 2014 – we have to have a sense of Christian compassion in taking care of people.
“No politician wants to say ‘I’ve got to make a tough choice here.’ This was a case of our endless poverty and we’ve come a long way in three years.”
Sinn Fein and independents were the big winners as the counting of votes in the Europe elections began on Sunday.
Luke 'Ming' Flanagan looks set to top the polls in Midlands-North-West while Sinn Fein could win a seat in all three Euro constituencies.
But the Irish Independent reports that Green Party leader Eamon Ryan has demanded a recount in Dublin where Sinn Fein’s Lynn Boylan topped the poll.
Fine Gael’s Brian Hayes and independent Nessa Childers were elected without reaching the quota but Ryan, just 1,149 votes behind Hayes and a further 193 votes behind independent Childers, decided to request a recount.