The Minister for Justice has said the European Court ruling that a Chinese woman whose baby was born in Belfast should be allowed reside legally in the UK, was further proof of the need to hold a referendum on citizenship.
Catholic Church lobbyists for the 11,000 people awaiting decisions on their deportations say their positions should be regularised.
But they point out that it is incorrect to describe this as an amnesty because the people in question did nothing wrong.
They applied for residency before the Jan '03 Supreme Court ruling when the policy at that time gave them a right to reside here with their Irishborn children.
Govt examines EU court ruling
The Department of Justice has said it is examining the preliminary ruling by the European Court of Justice.
Lawyers for Man Levette Chen had argued that because her child was an Irish citizen, she should automatically be allowed to reside in another EU member state.
The UK immigration authorities rejected this but the European Court's Advocate General has upheld her argument.
Irish body comments on judgement
The preliminary judgement should give the Irish Government the opportunity to fast-track the regularisation of families of existing Irish-born children, according to an official advisory body.
The National Consultative Committee on Racism and Interculturalism says that many of the estimated 11,000 people facing deportation because of a Supreme Court judgement are enduring significant hardship because of difficulties in having their cases processed.
The committee believes that if Ms Chen wins her case, these potential deportees would be entitled to acquire the right to residency in any EU country by travelling to Britain or Northern Ireland.
Meanwhile, Dublin's Catholic Emigrant Advice Agency has joined the Migrant Rights Centre Ireland in urging the Government to decide urgently on the status of the potential deportees.