They are not against the US constitution. The extraction of blood, DNA, and other physical evidence is not "testimony" and has never been federally barred. The DUI defense lawyer would have you believe it is a violation of 724.013 in many circumstances. However, that statute covers the police obtaining the blood draw without warrant. The blood warrant is just the same as any other search warrant as far as the courts (so far) is concerned.
The restrictions in 724.013 (and it's exception in 012(g)) do not apply.