The words "obligation" and "procedure" are somewhat incompatible. The 14th Amendment clearly says that such an obligation does exist. There clearly has to be some "put up or shut up" point where TSA has to show (I won't use the word "prove") that a passenger is a threat to aviation or allow them through. Now, there's definitely the practical question of what they might ask the passenger to do or how long it might take. We've heard numerous stories of people not being allowed through who refused to "cooperate" with TSA procedures, but I can't think of a single report of a passenger who submitted to those procedures who wasn't admitted, which suggests that it's extraordinarily rare. I've been told that a denial creates lots of paperwork and has to be done at the checkpoint at an STSO level or above.