If I recall correctly, and this is based on some old case law that I learned in high school, so bare with me a bit:

A suspicionless search is reasonable under the Fourth Amendment when it meets a balancing test as outlined in the Brow V Texas decision (1979). This balancing test is at its heart, three pronged and must balance the individuals right to personal security against these three prongs, namely: the state interest involved, the level of intrusion, and the effectiveness of the procedure. Or something like that. Well, in the case of Texas v Sanchez, the supreme court ruled that this balancing test was not violated, but this was only for road blocks in general. When the subject of road blocks for sobriety check points, in the decision of Michigan Police v Sitz (uh, 1990? I think), they ruled that sobriety check points satisfied all three prongs. So that's sorta the constitutional motivation for the 4th amendment violation. One might ask, how is a balancing test reasonable?! Well, the constitution protects the rights of our citizens as consistent with those of a Liberal Democracy. Well, the most general way to phrase the rights possessed is as follows: you have all the rights that you desire to accrue so long as the collection of such does not, in any way, hamper the self actualization of another. Said in a more concrete way, the rights of my person stop at your nose.

So, the 5th amendment? In Schmerber v. California the courts ruled that the privilege to prevent self incrimination extended only to oral and written communication and not to physical evidence. Furthermore, this wasn't a violation of the due process amendment (14) because it was done by a doctor in a humane fashion. IIRC, all these blood draws have to be done by a qualified medical technician blah blah. Some argue that this case isn't applicable to field sobriety exams as the draw occurred at a hospital but in the decision, the justices made it very clear that the 5th only applies to your written and oral communications. The 4th protects you from unreasonable search but we've already seen that.

Also of note: Blanton v. North Las Vegas says you're not required to get a jury trial with a DUI case California v. Trombetta Says you don't have to save the breathalyzer data, effectively violating the due process clause

Hope that helps. There's more case law out there but I don't remember it all -- American History was like 4 years ago man.

edit: oh and the other case I was thinking about for the fifth was South Dakota v. Neville, which held that it was not a violation to force someone to submit to breathalyzer or blood tests.