The Taoiseach has said the results of the Irish Times TNS/mrbi poll are disappointing but the Government will get on with its work.
Speaking in Clara in Co Offaly, Mr Cowen said he is determined to lead the Government in a way that will address the major challenges the country faces.
Mr Cowen said he was resilient in character and this was all part of party politics, but he was determined to continue to implement the policies that are necessary to make the adjustments to the economy.
When asked if he had considered a call for a General Election, the Taoiseach said he got a mandate to form the administration seven months ago and was only in the second year of a five-year term.
He said it was important for the public to remember that we have to implement the policies that are necessary to help the economy.
Earlier, Green Party leader John Gormley said it is very clear that the public's trust in the Government has been eroded following 'a very difficult Budget'.
Mr Gormley said he believed people were finding it difficult to accept that the country was in a very difficult economic situation and that there have been cutbacks.
He was reacting to the findings of the latest TNS/mrbi opinion poll for the Irish Times, which indicated that support for the Government has collapsed, with the level of dissatisfaction in the Government's performance at 76%.
Mr Gormley said the poll findings were understandable in the context of the Budget the Government had presented, but he expressed satisfaction that his own party's rating was relatively stable.
The coalition partner's rating is at 4%, down one point from the last TNS/mrbi poll.
He claimed that was a message from his party's supporters to continue with the work of implementing the programme for government.
Mr Gormley's personal satisfaction rating as Green Party leader is down 12 points to 28%.
However, he said he was not concerned by this because support for party leaders 'across the board' was down.
No time for Fine Gael triumphalism, says Kenny
Fine Gael leader Enda Kenny has said the poll is devastating news for Fianna Fáil backbenchers as it would imply more than 20 seat losses for the party.
However, he said the situation facing the country was too serious for any triumphalism on the part of Fine Gael.
Launching a post-Budget winter campaign for his party, Mr Kenny said his focus remained ensuring Fine Gael was the largest party in the next Dáil and returned to power.
Asked about the drop in his personal ratings, he insisted that his popularity was not important and said his priority was to lead and build Fine Gael.
Mr Kenny said defections from the Government ranks meant the possibility of an early election had increased.
The Fine Gael leader said his party was already in election mode with many conventions for the local poll next year already held.
Speaking in Galway this morning, Labour Party leader Eamon Gilmore said: 'If the results of the poll were repeated in a General Election the Labour Party would gain eight to ten seats.
'There would be a change of Government and, in all probability, the Labour Party would be in the new Government.'