The Minister for Education, Mr Dempsey, has said he would consider seeking the leadership of Fianna Fáil if he got the chance. He added that, if successful, he would retain the party's "slightly left-of-centre credentials".
He said the widespread belief that Fianna Fáil had misled voters in 2002 about the state of the public finances and the problems in delivering good quality public services were to blame for the party's poor performance in the June local and European elections.
In an interview in the Weekender newspaper in Navan he said the party should not be looking for "external scapegoats" such as the PDs for its troubles.
"We have problems ourselves. It is a bit like when Fine Gael were low in the polls, the first thing they started doing was looking to get rid of leaders.
"They managed to get rid of three of them within a relatively short period of time and they still proceeded to a point as near to electoral meltdown as makes no difference."
Asked by reporter Brendán Morley if would he like to be party leader, he said: "Any politician at my level who would deny that he would like to be leader of the party, well I just wouldn't believe them. If the opportunity arose, I would certainly consider it."
If he was leader, he said: "There would be an emphasis on social justice. From an economic point of view, I don't think that the direction of the party would be much different."
Mr Dempsey said: "[Fianna Fáil had\] gone as far as we should go in terms of lowering taxation. We need to keep our emphasis on a social-justice agenda."
He said he could see a Fianna Fáil/Sinn Féin coalition happening. "There is only one thing preventing that - the continued presence of the IRA. Once that is no longer an issue, it simply becomes a matter of whether a programme can be agreed."
Asked about his proposal to reintroduce third-level fees, which angered some Cabinet colleagues, he acknowledged that he might be "a bit impatient to get things done".
He said that despite the media speculation about whether he would retain his Cabinet post, "it is not something that I lie awake worrying about at this stage".