I support the Constitution of the United States. For that reason, I would be opposed to this type of widespread DNA swab type gathering of "information".
The fourth amendment protects against this. Period.
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http://www.archives.gov/national_archives_experience/bill_of_rights_transcript.html
Amendment IV
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
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I have broken no laws. I am not fearful of the police. Should I then be subject to being stopped on the street to contribute DNA? No.
There are instances where this is acceptable, but not in public. I am in favor, for instance, of mandatory drug testing in the workplace. Hell, I'm even in favor of testing everyone who receives any (and I do mean any) government funding - be it through employment, welfare, grants, etc. Not drug free, lose your funding....
You see, I am not afraid of drug testing because I am drug free. I would not want, however, to be stopped in the Wal-Mart and asked to piss in a jar. That would be unconstitutional.
Just my $0.02 worth.