I would stay away from the lawyer asking 40% for a law suit; although correct that law enforcement CANNOT ask for identification and proof of legal status without reasonable cause, if he was near a border crossing and "suspicious" in any way, then he may have a tough time proving Racial Profiling...i.e he would be paying the lawyer a whole lot of money without much chance of success at anything concerte.

Overstay is a major issue: depending on where you are in the U.S you may want contact some immigration based non-profits that could refer you to lawyers who knew what they are doing (i.e. will probably charge more than others but at least you know they will do a good job) Start calling places like the following and see if they can refer you to good immigration lawyers in their area.

National Immigration Law Center, D.C (213) 639 3900 

Catholic Legal Immigration Network Inc (CLINIC): (202) 635-2556

Good luck!