Seems that most on FR say driving is not a right but a privilege and therefore the above is not unconstitutional. Apparently it holds up in court, but I don't know the legal means. Same for road blocks.
Is welfare a right? Seems if you don't want a drug test, don't ask for welfare. Sort of how NYC got by with random bag searches at subway stations. If you didn't want to be searched, you had that choice, but then you couldn't ride the train. At least not at that station.
Maybe the drug test could be random prior to picking up a welfare check. You don't have to pee in the cup, but you're not going to get that month's check unless you do.