Police Force Blood Draws on Citizens

I didn't know this until today, but apparently law enforcement officers can forcibly draw blood from those suspected of a DUI after they get a warrant.

I fully admit that I'm not familiar with the laws and procedures regarding testing on DUI suspects, but this seems to me to a bit over the top, and really poses the question: Couldn't this be considered a violation of the Fourth Amendment? I would imagine a forced blood draw is an unreasonable search.

Of course it is my understanding that such forced blood draws are only done when a citizen refuses a breathalyzer. So what do you think? And before you answer, check out this video of an actual, forced blood draw recently done in Georgia. . .