"For instance, I'd wager you have no problem when the police swab a suspect for their DNA, nor when a passed-out drunkard is compelled to provide a blood sample in the hospital after a DUI..."
Certainly in my case I absolutely have a problem, and always have, with any of things happening without a warrant. The Fourth Amendment seems very clear: "The right of the people to be secure in their persons...", listing the person him- or herself as having a right to security first and foremost before any other item.
Yes, this has passed SCOTUS muster, but it boggles the mind how it could be read in any other way. Certainly I would vote against any such warrantless personal evidence gathering if I had a voice in the matter.