Taoiseach Bertie Ahern said it was unlikely that the situation relating to the undocumented Irish in the United States would be resolved before November's presidential election.
"All of the main players and all our supporters in both Houses of Congress have made that clear to us since last year. We were very disappointed that efforts by the US Congress to pass the comprehensive reform legislation were unsuccessful, because we had put a good deal of effort into that, as had members on all sides of this house," he added.
"However, we are continuing to explore bilateral options to regularise the status of the majority of the thousands of undocumented Irish, particularly those who have been in the US for many years, and to put in place an ordered system of legal migration from Ireland to the United States."
Mr Ahern said that the Government had engaged in wide-ranging consultation with members of Congress, the US Administration and the Irish community there, to assess how this might be achieved.
"There are strong differences of opinion, even among our supporters and people who have been very helpful to us over the years. I believe many people have been persuaded of the need to provide future opportunities for Irish people to work and travel in the US, which would also be open to the undocumented," he added.
"However, it will be extremely difficult to secure such an arrangement, given the nature of the immigration debate in Washington. For obvious reasons that are not Irish-related, this is a passionate and divisive debate." Mr Ahern said he did not believe anyone was against the Irish cause.
Fine Gael TD Michael Ring said that in the past month, a young Irish person, who was sick with pneumonia, could not go to the authorities or the hospitals because he was afraid he would be identified and sent home.
"He was sent home, but the problem was he came home in a coffin. That is sad. These are our citizens whom we must protect."
The caucuses were taking place in relation to the presidential election but the only person who was talking about immigration is John McCain, he added.
Mr Ahern said that support for Ireland on this issue was strong.
"Senator Clinton, Senator McCain, Senator Kennedy and others are strong supporters. For understandable reasons, and I understand them totally, all of them had to get off the bus on this issue last year and nobody more so than Senator John McCain.
"Senator John McCain took a very forward view but he had to reverse at high speed and I understand why. I think, however, at another time he will come back as a supporter." Mr Ahern said that the Kennedy-McCain relationship had almost worked.
"It was a pity it did not, but we will have to come back on that. We all know the game and I am afraid the game will not resume until next year."