Minister of State Conor Lenihan has said Taoiseach Brian Cowen should resign.
"It would be in the best interests of the party if Brian Cowen moved on because it is not working out,” he said.
Mr Lenihan said the Fianna Fáil leader had lost the confidence of the party and the people.
He said events over the last 24 hours had raised an issue about Mr Cowen's leadership once again and that quick action was needed by senior members of the party.
Mr Cowen's authority and credibility had been eroded over the last few days and many people who voted confidence in him are now thinking quite the opposite, the junior minister said.
“The only way this can be resolved is if Mr Cowen thinks about the position he has placed the party in and takes the kind of resolute action that I think people expect him to take,” Mr Lenihan said.
Separately, backbench TD Tom Kitt said he was "infuriated" by what had happened.
"This has totally backfired, I've been in the Dáil for 23 years and I have never seen anything like this," he told RTÉ.
"I'm really infuriated by what's happened. It has been totally mismanaged and the main things that's come across is that there is a total disconnect with the leadership of my party and the public out there. People are rightly very upset."
Additional reporting: Reuters