It's probably not correct that Obama could close down the entire NSA tomorrow. However, he has essentially complete control over what it does. If he wanted to direct it to do, for example, only military intelligence activities directed solely at warfighting intelligence, he could.

This Executive Order:

http://www.archives.gov/federal-register/codification/execut...

can be changed at any time and to whatever the President desires it to be. He could change it this afternoon if he liked.