Sure, but also notice how they never (in history) tried to control your dollars in such a manner.
If they had set their mind to do just that, I bet they would succeed. For one: forbid all cash, arrest at once anyone using or accepting it (or any self issued barter system) and only allow credit cards and e-money.
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, etc., etc.