A poll of polls prepared for RTÉ has found significant falls in support for the two Government parties.
Compared to the 2011 General Election result, it found Fine Gael could lose up to one-third of its support.
Labour could lose up to two-thirds if the voting intentions are reflected in the weekend election results.
Over the course of the election campaign several polls have been published by all the major polling companies.
The poll of polls for RTÉ on the national "state of the parties" based on a sample of over 5,000 shows Fine Gael at 24%, down 12 points since the General Election.
Labour is on 7%, also down 12; Fianna Fáil is on 22%, up five; Sinn Féin on 22% up 12, and Independents and Others are on 26%, up eight.
A second poll of polls, based on a sample of over 9,000, compares national European election voting intentions with the 2009 European Election results.
It shows Fine Gael at 26%, down three since 2009; Labour at 7%, down seven; Fianna Fáil on 23%, down one; Sinn Féin at 17%, up six, and Independents and Others at 27%, up five.
The polls were prepared by Professor Michael Marsh of Trinity College Dublin with the co-operation of polling companies Millward Brown, IPSOS/MRBI, Red C and Behaviour and Attitudes.
Meanwhile, Taoiseach Enda Kenny has said there will not be a renegotiation of the Programme for Government.
He was speaking at Fine Gael's final press conference before the Local and European Elections on Friday.
Tánaiste Eamon Gilmore also confirmed there will not be a renegotiation of the Programme for Government after the elections.
However, he said a reassessment of the existing priorities of Government will take place instead.
Speaking after canvassing voters in Kinnegad, Co Westmeath, Mr Gilmore said the polls indicated that Emer Costello and Lorainne Higgins were not ruled out of wining seats in the European Parliament.
He said Labour would canvas hard all the way to Friday's poll.
Earlier, Minister for Transport Leo Varadkar said it is not unusual for governments to lose support in mid-term elections.
However, he admitted the past couple of months have been difficult for the Government, particularly with issues around gardaí and justice.
Mr Varadkar also said the outcome of the Local and European Elections would not dictate the next General Election results.
Sinn Féin leader Gerry Adams has said he cannot say whether his recent arrest damaged the party's election campaigns, as he had claimed it had been intended to do.
Mr Adams maintained his detention in connection with the death of Jean McConville had only been raised in a kind way by people. He said they told him they were glad he was released.
Meanwhile, Minister of State Jan O'Sullivan said Labour knows it is not at the point it was at during the last election.
She said the party has had to do a lot of unpopular things because of the Troika agreement, and although the economic recovery has started, people do not feel it in their pockets yet.
This evening Mr Kenny refused to say what instructions he had given the general secretary to the Department of Justice before sending him to visit former garda commissioner Martin Callanan on the evening before his resignation.
Speaking on RTÉ's Six One News, Mr Kenny said he would respond fully to such questions before the Fennelly Commission of Investigation.
The Fine Gael leader said that people can see the change in the economy that has seen the creation of 1,200 jobs each week.
He said he had taken over a country with an unprecedented economic catastrophe that required and continues to require difficult decisions.
He is aware that many hundreds of thousands of families are strained with their finances each week and it has been very difficult, he added.
Mr Kenny also said the issue of discretionary medical cards will be dealt with after this week’s elections.
MEPs who lose seats entitled to transitional allowance
MEPs who lose their seats in this weekend's election will receive a transitional payment equivalent to a year's salary phased over up to two years after they lose office.
The European Parliament Information Office in Dublin has confirmed that at the end of their term of office, members are entitled to a transitional allowance, equivalent to their salary, for one month per year they were in office.
However, this allowance cannot be paid out for longer than two years.
The allowance is not paid if an MEP has a mandate in another parliament or takes public office.
In addition, if the MEP is simultaneously entitled to an old-age or invalidity pension, she or he cannot receive both and must choose one or the other.