This and the fact that Obama is constantly being caught in lies says to me that the U.S. government has no clue what information Edward Snowden has passed off to Greenwald.
I could see this being the case because politicians train to talk about health care and the economy, while the details of NSA programs are rarely discussed and so politicians have little incentive to be up on the facts.
It's quite probable that Obama knows about shit the various agencies have done that would make GG's hair curl. It's also quite probable they've done much worse shit that he doesn't know about.