Taoiseach Bertie Ahern faces little or no significant pressure from within the Fianna Fáil parliamentary party to step down quickly, according to an RTÉ Prime Timepoll.
Thirteen of 42 TDs and junior Ministers who responded to the poll believe that Mr Ahern should step down within the next two years, though three of them favour him going after the local elections.
Four felt that he should go within the next year; nine believed he should step down within two years; and 17 felt that he should go "sometime" after two years.
Thirteen of those questioned believed that someone other than Mr Ahern should lead Fianna Fáil into the local and European elections in 2009. Eleven of them favour Brian Cowen to replace him.
Twenty-three others, however, said that Mr Ahern was the best person to lead the party into the June 2009 elections.