What is the inherent problem with illegal immigration?

[W_HAMILTON]

This may sound like a dumb question, but what is it really?

Obviously illegal immigration is not ideal, but I don't understand why it is such a massive problem. I asked some people, and they said "crime."

Well, if crime is a problem, how does having the police check people for citizenship solve this? Instead of preventing or stopping crime, police are now going to be tied up making sure everyone they pull over has their papers in order. How does this help stop crime? If the police find illegal immigrants even 90% of the time, that still means 10% of the time they are unnecessarily wasting time checking on the status of legal citizens of this country. That time could be spent patrolling or other means to prevent crime.

Also, what are they going to do with these individuals if they find them to be illegal? Lock them up forever? One year? One day? Just take them back to Mexico? Unless the penalty is harsh -- which I don't believe it is -- the illegal immigrant can simply come back illegally once he is released.