Commenter JP has it right: The Providence Phoenix profile of the Providence diocese’s immigration point-woman Stella Carrera is yet another litmus test on the issue. Consider one of several stories from her clients:

One of the faces Carrera knows is that of Carla Rodriguez (not her real name), a 42-year-old Guatemalan native who has been in the US illegally since 1994.
At that time, Rodriguez, her husband, and her five children flew to Mexico and walked across the border into California. Rodriguez was eight or nine months pregnant. A week later, she gave birth to her sixth child. The family flew to Providence to be with Rodriguez’s brothers and sisters, who had moved here years earlier. Her husband worked as a locksmith, and her children began to attend public school.
The family has lived in fear for 13 years. It makes them nervous even to be out in the streets.
They are afraid they will be stopped and deported. They don’t go out, except to go to church, to the grocery store, and occasionally to visit relatives. The children do not work, or go to parties. They come straight home after school.

Of course we’re rightly sympathetic to the difficult position in which their immigration status places the children, but where’s the admission of culpability from the parents? Do they ever feel a pang of responsibility for having brought six children into circumstances that require them to keep such a low profile? Clearly, they find it to be a more attractive option to support a family of eight on a maximum salary (as reported) of $18,200 in the American shadows than in the broad daylight of Guatemala, but where’s the gratitude to the society that has picked up a tab that surely amounts to many times that?
Another woman left her son in El Salvador and sends him $50 a week from a $15,600 salary. While in Rhode Island, she married an illegal immigrant (who, tragically, was murdered by robbers subsequent to his deportation), with whom she had two more children. The woman appears to be in the country with refugee status, but it’s notable that she hasn’t bothered to learn the language of the country that is protecting her during her 12-year stay.
Bishop Thomas Tobin frequently cites Jesus’ suggestion that helping strangers is tantamount to helping Him, but it’s difficult to see the lesson as applying to such cases. How many working class Rhode Islanders must live that much closer to the edge — some certainly slipping off — to ensure that their state remains an international beacon to large families that take up residence for the duration of their children’s education? There must be moral obligations on such families — to acclimate, to contribute, to appreciate, to minimize the burden — but I just don’t think I’ve ever heard immigration advocates enunciate them.