Indeed. I'm not quite sure why people think the government doesn't already a "national database of citizens" between social security (theoretically assigned to every citizen) and taxes (ties SSN to address yearly).
The latter kind of knowing is what we're afraid of, especially the database of faces.
How this information is disseminated within the federal government or between states sounds like an excellent debate to have, as does the discussion about due process for suspects... but 'should the government be able to know who it's citizens are' is a silly one.
Participation in the Social Security program is optional.[0]