Suppose you're a Foreign Terrorist. If you're planning an attack on the US, can you do it entirely from your country? At some point you have to contact some people in the US to carry out the attacks. But oh, the Americans you hired are very wily, and they know that, to be relatively anonymous and have their shenanigans hidden, they have to call from different phones, send emails from different accounts, use different identities, encrypt everything...

Mr. American Terrorist Contractor can't have all his communications tied to a single identity that could be reassembled with Big Data. So he tries to keep very few traces of his activity, and confuse snoops with false leads and dead ends.

Mr. American Terrorist Contractor called from many phones, used many addresses, etc. The dragnet to catch him must be large. It will include some innocent Americans. Tens who called a phone he called that same day. Hundreds who went to the same deli as he went last Friday. Add more situations, area codes, phone call graphs and quickly you have most Americans.

That's by design, though: you can't have surveillance that's capable of catching domestic terrorists without surveilling innocent citizens, and you can't try to end terrorism with surveillance without spying on the people who will actually perform the terrorist acts in your land.

EDIT: As it currently stands, the NSA is supposed to help end terrorism by spying on all foreigners. What I'm arguing is that surveillance of non-citizens always leads to surveillance of citizens. Some Americans are uncomfortable with the US government spying on American citizens, but comfortable with the USG spying on foreigners. They may be less comforted when they realize how, if the real intent of the surveillance is to prevent terrorism, only spying on foreigners won't help much.