What about using public APs from a distance (cantennas are easy enough to put together), a live OS and a spoofed MAC address? As long as you leave your smartphone/tracking device at home and compartmentalize your activity (ie, don't visit sites or use logins you use in your day to day online interactions), I would think that it would be extremely difficult to link traffic with a person.
More involved exploitation and monitoring (such as malicious files) would probably mean that there is an actual agent or agents interested in your activity. Unless you're into some serious naughtiness or a Muslim (and even those people aren't monitored very effectively [the Tsarnaev bros. come to mind]), I wouldn't anticipate the NSA purposing those limited resources to users. I think with open source software and a little bit of cryptography, you can subvert most of the dragnet data mining tactics in place.
And as a government employee myself, I can say that we are far from the hardest working demographic. I wouldn't be surprised if the vast majority of individuals flagged by whatever magic 8-ball algos are in place in NSA datacenters go without investigation.