The NFL game feed is a combination of a couple of feeds. There's
http://www.nfl.com/liveupdate/scorestrip -- which will show you the events and IDs that are currently going active. Right now, in the off-season, it will undoubtedly be blank. You can then take those values and plug them into this one:
I don't remember the one for the NBA, as I've never used it, but I saw an article on reddit a few weeks ago about how to get the data from the NBA using their RSS feed, so I have a good faith belief that it exists.
Thanks for sharing this! The only thing I had found was stuff like SportsXML, etc. but it took me weeks to just get a demo data dump for a single game and the pricing was way too much to bite off.