Many of the illegal immigrants are NOT from Mexico, they are from other countries south of the border.
Here in Dc, most hispanics are NOT Mexican, they are usually from El Salvador, also Nicaragua, Columbia, , ect...
The ones from El Salvador tend to cause a lot of problems. Not all of them, of course. I know several who's parents made them learn English, go to college, ect... But far too many of them go the other route, know what I mean? Gangs, violence, teenage motherhood...you know the routine.
Anyway, most of them take a bus from El Salvador to somewhere in Mexico, then walk the rest of the way.
And yes, they do have a devastating effect on our healthcare system (though they are not the only group who does so).
However, young doctors and nurses who work with them (in maternal medicine, that is) get to learn a whole lot real quickly; it's very "hands on" learning, a sort of "baptism by fire", as these women do not pay and must rely on student and resident doctors to deliver their babies. When I was a nursing student, the first birth I saw was attended only by me and a medical student.
Sure, there was an older doctor present on the floor somewhere, but he can only be in one place at one time, and there were probably 6 other uninsured women in labor at the same time.