In order to keep from being deported, a person would have to prove legal status and if you don't have a legal, verifiable national picture ID for all adults living in America then how do you confirm that?
All existing ID's don't prove citiznship(as we have learned the hard way).
In order to keep from being deported, an illegal will evade law enforcement (which the national ID card wont stop) as they are doing now or forge this new national ID card. EVERYTHING is forgeable, especially when there are people in the border patrol agency, DMV and other agencies that are sympathetic to the cause of illegals.