The first national opinion poll since the controversy over Taoiseach Brian Cowen's Morning Ireland interview shows that 71% of voters believe he has lost credibility as a result.
However, an even larger majority said they will not change their voting intentions.
The poll also shows a large swing in support to Labour, which emerges as the party with the largest support.
The Millward Brown Lansdowne poll for TV3 News shows that a majority, 56%, believe the controversy over last week’s interview with Mr Cowen does not matter and 88% say it will not change their voting intentions.
1,000 voters nationwide were questioned on Tuesday and Wednesday for the poll.
40% said Mr Cowen should continue as Taoiseach, while 52% said he should not.
In terms of party support, compared to the last Millward Brown Lansdowne poll in February, support for Fianna Fáil is down 5% to 22%; Fine Gael is down 4% to 30%; Labour up 16% to 35%.
The Green Party is unchanged at 2%; Sinn Féin down 4% to 4%, and Independents and others are down 2% to 8%.
Commenting on the poll, Government Chief Whip John Curran said: ‘This poll mostly reflects trends already reported by other companies in the seven months since Millward Browne last published a poll.
‘Our position on bad polls is exactly the same as it is with good polls; they are interesting but have nothing to do with getting on with the business of taking the right choices for the country's future.’