But it can be prohibitively difficult. If you're solo-mining coin, its going to be almost completely untraceable. Mining via a pool might be tracable depending on what contact details you disclose and whether the pool logs your IP address (and is subpoena'd to disclose it).

Of course who knows what the NSA are logging, but since they deny everything, you'll probably get away with it unless you're on their hit list (then maybe expect a visit from a nice shiny drone).