Senior figures in Fine Gael and Fianna Fáil have insisted they would never enter any coalition with Sinn Féin, irrespective of their leader.
Sinn Féin passed a motion at its ardfheis this weekend allowing it to enter government as a minority partner, a significant shift by the party.
However Taoiseach Leo Varadkar and Fianna Fáil leader Micheál Martin ruled out doing business with Sinn Féin.
Mr Varadkar said the party "might be getting younger but their policies are the same". His view was echoed by senior figures in the party including Minister for Justice Charlie Flanagan and Minister for Social Protection Regina Doherty.
Mr Flanagan said: "From a policing and a security point of view, Sinn Féin is not fit for government. It also engages in Paul Daniels economics," he said, referring to the magician.
Ms Doherty said the main contender for the leadership of Sinn Féin, Mary Lou McDonald, has sought to “defend the legacy of Sinn Féin and the IRA”.
The Minister pointed to Ms McDonald's loyalty to Gerry Adams when he was being accused of covering up sex abuse allegations.
In a speech on Saturday night, Fianna Fáil leader Micheál Martin strongly criticised Sinn Féin for always “putting the Provisional movement first”.
He added: “They might be new leaders but they are not new faces. For one moment let’s assume that Sinn Féin will act against type and actually hold a democratic election for its next leader.
“The fact is that every one of their potential leaders joined Sinn Féin before the ceasefires and has repeatedly defended the Provisional IRA’s campaign.”
A number of Fianna Fáil TDs have spoken in favour of a coalition with Sinn Féin. However, party spokesman on housing Barry Cowen urged “such troublemakers” to remember the vote taken by the ardfheis earlier this month.
The Fianna Fáil conference agreed not to enter any coalition arrangement with Sinn Féin. Mr Cowen insisted there would be no deviation from that policy by the party.