@Reminiscence, my great-grandparents were some of those immigrants who arrived here by ship around the turn of the Twentieth Century. They were glass workers back in Slovakia, and a glass company in Toledo, Ohio was hiring as many experienced glass factory workers as they could afford. Their paperwork and immigration status weren't nearly as important as the skills they brought with them.
In my opinion, that's the difference between those immigrants of the past and the so-called illegal workers today. Back then, the jobs those immigrants were doing, like steel work, glass making and brick laying, were seen as a noble thing. They were helping to build America. But now the perception is that these illegal immigrants are stealing jobs from Americans.