Mr Rabbitte cited the impact of the referendum on the Good Friday Agreement (GFA) and strong reservations expressed by senior political and human rights bodies as reasons behind the hardening of his opposition to proposals to restrict the rights of citizenship for children born to non-national mothers.
But in an immediate response last night, Education Minister Noel Dempsey rejected Labour's criticisms and insisted the referendum would not be delayed or postponed. He also maintained that it would have no effect on the Agreement.
Until yesterday, the Labour Party leadership has confined its criticisms to the scheduling of the referendum for the same day as the local and European elections. The party has claimed that the June 11 date was chosen for cynical electoral purposes by the Fianna Fáil-PD coalition.
The ratcheting-up of the war of words came as SDLP leader Mark Durkan made a blunt appeal to the Government to postpone the referendum.
Mr Durkan, who has written to the Government expressing his concerns over lack of consultation, said the amendment would cause difficulties for the Constitution and for the democratic process. He suggested the amendment be referred to the Forum for Peace and Reconciliation.
"The Government knows from how European referenda were conducted in the past that when things are done without full consideration, and without thinking through all of the issues, you can get into difficult situations," he said.
The Government yesterday declined to comment on the stance Labour has adopted. A spokesman said there would be an opportunity for opposition parties to be briefed by Justice Minister Michael McDowell this week. He also said that Taoiseach Bertie Ahern would be replying to Mr Durkan's letter.
Mr Dempsey, speaking on RTÉ's The Week in Politics, said the SDLP had been informed of the proposed changes at the same time as all other parties.
He said the referendum would bring a legal certainty that would be "more in line with the GFA than the current situation".
Yesterday, Mr Rabbitte renewed his attack on the Government, accusing it of rushing the referendum to shore up support for Fianna Fáil in the local elections.
"I was determined until now not to let the debate get onto the substantive issue because I feel that it is necessary to expose the base motives behind running a referendum like this in the context of an election," he said.
He accused Mr McDowell of being misleading as well as being high-handed and arrogant in approach.
"He does not like being caught out," Mr Rabbitte told RTÉ radio. "He is the brightest boy in the class who has been exposed as telling fibs that would compete with any of his FF colleagues."
Several senior figures in Labour, including party president Michael D Higgins and Proinsias de Rossa, also made outspoken criticisms of the proposals during Labour's national conference in Dublin.
The proposed Constitutional amendment will be debated over two days in the Dáil this week.