Can a U.S. citizen make a citizens arrest on an illegal immigrant?

I was asked this question by my wife. i thought it was a good enough question to ask on Fluther. most states have citizens arrest laws. this is where a citizen witnesses or suspects someone of violating or commiting a crime. does the citizens arrest law allow citizens to stop and question suspected illegal immigrants, since the police cannot? citizens actually have more power, in this situation, than the police. once the citizens arrest is made, the suspected illegal immigrant would be turned over to the police. i am on the defensive, when i ask this question. i feel that this may be the future for U.S. citizens. i hope not. so, whats your opinion?