The president can't arbitrarily shut things down or have much direct control. Congress both controls the purse strings and requires money to be spent. At best, POTUS can generally enforce the law, but NSA actually has authority to do mass surveillance from Bush era laws.
That said, Obama is clearly in favor of surveillance.
You do have to wonder what exaggerated lies they're told to believe that such surveillance is even necessary. I say lies, because if there were any real threats so many more terrorist attacks would happen than actually do.
The other theory I've seen is that people in power are used to having their life scrutinized publicly, so personally don't really care about privacy, so are the worst people to making decisions about such things.
I think it's more of an incentive problem, after a disaster like say Hurricane Katrina it's really hard to stand up and publicly say everything is working just fine.
Ideally, you want to be able to say well "where it not for the other guy we would have implemented my solution!" Which creates huge pressure based on how bad things look vs. how they actually are.
That said, Obama is clearly in favor of surveillance.