(Cue Evil Laughter) The original video can be found here. But the video file at LiveLeak is bad.
Here is his description from LiveLeak:
There is a popular video that pops up every now and then that has John F. Kennedy making allusions to a secret society and other kinds of woo woo.
That speech has nothing to do with the NWO people. He means communism and he was addressing the American Newspaper Publishers Association and their responsibility to consider national security when publishing articles about government activity during the cold war.
Here is a link to the full transcript, where you can also listen to the fill 19 minute recording.