Not to put too fine a point on it, but using the term "criminal alien" the way you do reeks of ignorance. For one, immigration law is civil, not criminal, so when someone comes here illegally they are not even breaking a law (except now in Arizona, of course, which is why it's such a big deal that they made it a crime to be in Arizona if you are in this country illegally).
If an illegal alien is deported, and then is caught here a second time, then it's a felony and if prosecuted and convicted, it would then be correct to call them a criminal alien, but again, only after they have been convicted of being here a second time, or convicted of some other crime.
For the first offense, since it's not criminal, that's why they aren't subject to (nor can they demand) due process before they get deported. If we say you're out, you're out. If we criminalize that first offense, then each and every deportation will require a trial before a judge and jury. Be careful of what you wish for.