I guess there's a law that these folks have broken, but I've never heard which one. Quick googling gives no answers (to me, at least).
There's a misconception that being here on an expired visa (or no visa at all) is illegal, but I believe that the INS considers such a person to be "without status". And an alien without status can be deported.
Consider a young married couple...
Jack and Jill are college students. Jill is from Ireland on a student visa. Jack and Jill get married after graduation. Jack gets a job in Pittsburgh and they move into an apartment. Omigod! Is Jill an illegal immigrant? No, she's just without status.
Marrying a citizen does not automatically turn a foreign national into a permanent resident. Jack must petition for permanent resident status for Jill, Jill must apply for permanent residency, and Jill's application must be accepted. (And twenty years ago, Jill's application would be made and processed in Ireland... but that might have changed by now.)
Maybe a foreign national who is "without status" has broken a law, but I sure don't know what it is.
Using a forged Social Security card
is, on the other hand, a felony. And that's what bothers me the most about this illegal-immigrant-hairball. They're coming here for jobs. To get a job, they need a Social Security card which they present to their new employer. The employer fills out a form and sends the (forged) Social Security number and the name of the (now illegal) employee to the INS. Doesn't the INS cross-check this information with the Social Security folks?
Gee, it seems that Miguel Mendoza is currently working fifteen jobs in three different states! He's quite the go-getter!
And to speed things up a bit, why can't the employer be required to call an 800-number to perform a rudimentary verification of the Social Security information? That would nip a lot of this in the bud...