The Fine Gael leader, Mr John Bruton TD, said today he was "quite disappointed" at the result of today's Irish Times/MRBI poll.
The poll gave Mr Bruton a satisfaction rate of 37 per cent, his lowest rating since he was elected Taoiseach in 1994.
The Fine Gael party received a satisfaction rating of 20 per cent, a drop of four per cent.
Mr Bruton said the present government had received a "bounce" from the recent budget, which put a lot of money into the economy.
Asked about his own position, Mr Bruton said he not expect any challenge from within his own party to his leadership.
"The party made a decision on my leadership less than two months ago by a vote of three to one," he said.
He added it would make "no sense" to challenge him now.
Mr Bruton said he was "looking foward" to the next general election, and predicted that Fine Gael would gain seats in Dublin, Kerry South and Limerick East.
The Fine Gael leader was speaking at a forum organised by the party to discuss the current BSE crisis and was attended by thirty organisations including beef producers, promoters and public health experts.