Our own history, as well as that of other countries, shows that governments tend to use the powers, information, and tools available to them to deal with the problems of the day, sometimes because the public demands, in the heat of the moment, that they do so, without fully considering the consequences. Thus Congress authorized the use of Bureau of the Census records to round up Japanese Americans during World War II, and more recently permitted the use of information from social security records to track down evaders of draft registration. To control this tendency, we define and limit the powers we permit our government to exercise; that is what the Constitution is all about.
A centralized national identity system is an extraordinarily powerful tool to give to a government. No totalitarian government operates without one. It requires a naivete based on a total absence of historical perspective to believe that we can allow the government to establish such a system and at the same time prevent its eventual use for purposes that we would today consider totally unacceptable. The problem of illegal immigration does not warrant such a risk.