But most of them aren't the problem. No one complains about the Poles overstaying their visas in Chicago.
And many of them stay a short while and return home (like many European immigrants did in the 19th century).
The three biggest immigration problems are: a) Mexicans flooding the low-wage jobs and lowering wages further; b) the H1B visa scam depressing wages at the top end; c) Chain migration.
We need a moratorium on ALL immigration until we can figure out what's best for the country and how to best control our borders.
Again, none of those things are the problem (although you could make a case for H1B abuse) rather they are the symptoms. The problem is a lack of economic growth to absorb new and current workers.