Of course they should be deported, right after they serve some time for breaking our laws by entering this country, they should also have to pay restitution for the costs incurred. We could start a whole industry based on prison labor, you break our laws and we will work you hard for a few years and throw you back to your home country!
Illegal immigrants are just that--they are in the United States illegally and should be deported to their countries of origin. Convicted criminals should be deported unless they were convicted of extremely violent crimes such as rape, murder and violent assaults. Deportation is the legal solution to deter future illegals from entering the United States.
If someone has entered the United States illegally and is convicted of a felony or misdemeanor crime should have to serve the appropriate sentence rather than facing deportation. A murderer should not get to escape justice through deportation.
After they serve the sentence it would most likely be appropriate to deport the individual and return them to their nation of origin.