The Government must try to orchestrate agreement on the new European Union constitution during Ireland's EU presidency, Fine Gael strongly argues.
The Fine Gael Leader, Mr Kenny, said the Government could not "sit back" if the Taoiseach is to have any hope of concluding a deal before June. "I want to see agreement reached as soon as possible on anything that will make the EU more effective, efficient and accountable," Mr Kenny said.
Ireland now has "a great opportunity" to show new EU states that small countries "can heal, change, persuade, mend and even create a better Europe", he said.
However, Fine Gael TD Mr Gay Mitchell warned that the proposed full-time President of the European Council could threaten the existing balance between EU institutions.
"If the chair of the council oversteps his or her terms of reference, the Taoiseach should consider giving national parliaments a role in vetoing or removing him or her," Mr Mitchell said.
Meanwhile, Fine Gael's Mr John Bruton, who sat on the Convention on the Future of Europe, said Mr Ahern's push to settle a new Treaty must take place before March.
"If he does not fix it up between now and March, we will be going straight into the European Parliament election campaigns," said the former Taoiseach. A delay could be disastrous because the Treaty talks will become "entangled" in the negotiations due next year on the EU's budget for the rest of the decade.
The Dutch, who will assume Presidency after Ireland, want to cut their EU contributions, so their attitude will colour Treaty negotiations if the issue is left over until then, Mr Bruton said.
The Labour Party has also urged the Government not to back away from the Treaty despite the failure of the Italians to broker a deal in last month's EU Summit.
The Labour Leader, Mr Rabbitte, said Mr Ahern clearly regards the Treaty "as a poisoned chalice" that he wished to pass from him "as quickly as possible".
"There are real grounds for concern in the image so far created, if the image reflects the reality, that the Government seems prepared to avoid these issues during the Presidency," he said. Urging Mr Ahern not to prepare for failure, Mr Rabbitte went on: "Endless talk about the need for a period of reflection will do nothing to solve the problem." The Convention on the Future of Europe could be reconvened to offer possible solutions to the impasse revealed during the Brussels negotiations.
"The Convention was an unprecedented exercise in democratic consultation and virtually every political view in Europe was represented. It reached a remarkable degree of consensus." Meanwhile, the former Labour Minister for Finance, Mr Ruairí Quinn, said the Government could not ignore the weaknesses exposed in the EU's Growth and Stability Pact. It is essential that Pact is made to work, or rewritten to meet the needs of the 12 Eurozone states and others that would like to join, he said.
Welcoming the failure of last month's Brussels talks, Sinn Féin adopted a noticeably different attitude to the prospect of an EU constitution. "The Government should regard the Irish Presidency as a positive opportunity for reassessment and re-evaluation of the entire constitutional project," said Mr Caoimhghín Ó Caoláin.
Though the EU's existing rules must be simplified, he said negotiations cannot be used "to diminish national sovereignty and increase the power of the EU".
"We are opposed to the development of the EU into a state and do not, therefore, accept the argument that it must have a constitution.This fundamental question must now be reopened during the Irish Presidency. The breakdown should be regarded not as a hitch in some inevitable process leading towards a single state but as an important crossroads and a chance to choose a new direction." The Brussels talks had exposed the reality: "We saw once again the larger states attempting to assert their dominance through the adoption of a new voting system which favoured them."
The Green Party said the Government must insist that each member-state continues to have a member of the European Commission. "We are concerned that a President of the EU has been introduced despite that this was not specifically sought by most member-states," the Green leader, Mr Sargent, said.
The Greens are also unhappy that the six-month rotating presidency is to be abolished, and replaced by three country teams, "although it has proved to be extremely effective".
Urging Mr Ahern to push for a new EURATOM treaty to govern the EU's nuclear industry, Mr Sargent said the Government has done too little to date.
"Ireland's poor running on this is a disgrace given that the spectre of Sellafield is so close to us. We need to insist on a "sunset" clause as a bottom line," he said.
Meanwhile the draft defence agreement is sharply questioned by the Greens, particularly a clause that commits member-states to assist countries under terrorist attack.
"This clause, and the inclusion of the issue as appropriate to terrorist threats, bears an unfortunate resemblance to the pre-emptive doctrine of the United States," he warned.
The Independent TD, Ms Marian Harkin, said some voters in Ireland and elsewhere now believe that the EU is "going too far, too fast".
"We have just voted twice on the Nice Treaty. We are barely out of the polling booths when we are being asked to vote on a new constitution for Europe. For many Irish people, in particular, there is a sense of unease," the Sligo/Leitrim TD warned, adding that the new Treaty is already being greeted with scepticism. "Even the word 'constitution' is too much for too many people, especially those who changed their vote between the first and second Nice Treaty referendums," she went on.