In the US, President Barack Obama issued an executive order in November 2014 aimed at streamlining 11 million undocumented people there.
The action is aimed at accounting for those who have been in the US for several years and have not been able to pay all their taxes - but it will also pave the way to deport those convicted of felons and who may be deemed a security threat.
There are some 40-50,000 Irish who are working illegally in the US, and who will be able to avail of this legislation if and when it is passed.
Shona Murray reports from Chicago - one of the most Irish cities in America. She has been speaking to some of those affected.