Doesn't the US have some sort of "fourth amendment" which prevents surveillance of its own citizens (who might become terrorists)? And, unlike spying on internet usage, people are going to be really aware of drones buzzing them.
No, it does not. The Fourth Amendment prevents "unreasonable searches and seizures" -- there is no explicit right to privacy in the US Constitution. The Supreme Court managed to find one, though (via a "penumbra of rights"), for a specific politicized purpose, but hasn't been willing to take it seriously otherwise.
There are a few current court cases against the NSA surveillance in the US, but none got anywhere so far.
Yesterday I was using the Global Terrorism Database to check some suprisingly low figures on what percentage of terrorist acts are committed by Muslims. (Short answer: Worldwide since 2000, about 80%, rather than 0.4 - 6% as given in various sources.) But I found some odd patterns in the data for the United States. Look at this chart of terrorist acts in the US which meet GTD criteria I-III and are listed as "unambiguous":