It can't just be "deportation", though. The penalty for stealing a car isn't just that you have to give the car back. The punishment for being found in the country illegally has to be severe enough that people are actually discouraged from making the attempt (or to deport themselves if they're there at the moment).
In Australia, our illegal immigrants tend to wind up spending a long time in an immigration detention centre while awaiting trial, which is strictly speaking an administrative need but winds up working as a pretty good punishment. I'm not sure if this scales up to the American system though as you have a lot more people you're gonna need to process.