The Socialist Party has called for a referendum to be held on the outcome of the European summit.
Socialist TDs Joe Higgins and Clare Daly and MEP Paul Murphy claimed the EU deal will entail a significant transfer of power from the Dáil to the European Commission, European Council and European Court of Justice.
The party said it would campaign for a no vote if a referendum is held.
Meanwhile, Fianna Fáil's Finance Spokesman Michael McGrath has said the decision by the Britain to opt-out of the new fiscal arrangements across the EU could have serious consequences for the future of Ireland's financial services industry.
Deputy McGrath warned that Ireland could soon have a situation where its financial services industry would be subject to a new transactions tax, but the City of London would be exempt.
He called on Taoiseach Enda Kenny to state clearly what the implications of such a tax would be for Ireland.
US welcomes eurozone progress
The White House has said signs of progress in the fight to end the eurozone debt crisis were "a good thing", but a spokesman added that work remained to be done.
The comments mark the first US reaction to the Brussels summit of EU leaders, who agreed to back tighter budgetary policing in a bid to save the eurozone.
Meanwhile, the top military commander in the United States, General Martin Dempsey, said he was concerned about "the potential for civil unrest" as Europe's financial crisis continues to unfold.
General Dempsey said it was unclear if the latest steps taken by EU leaders would be enough to hold the eurozone together, adding that a break-up could have consequences for the Pentagon.
26 of the 27 EU states have agreed to forge a tighter fiscal union however the United Kingdom refused to sign up to a new treaty, citing national interest.
General Dempsey, who is chairman of the Joint Chiefs of Staff, told an event hosted by the Atlantic Council, a Washington based think-tank, that "the eurozone is at great risk."
He suggested that part of his concern was that the US military could be exposed to any unravelling of the eurozone "because of the potential for civil unrest and the break-up of the union".