For now we're cheating and using a thing called TextGrabber (we were in a rush for the debates and couldn't play with more direct software solutions, but those absolutely exist). The box costs about $300 :: http://www.textgrabber.com/

If you wait I'm sure I or someone will add the ability to use a video stream as a source; there are tools out there that pull Closed Captions from video files and streams. For instance http://ccextractor.sourceforge.net/

Heck, maybe you want to add that feature :)