Thanks: jct74 @ LibertyForest
Internet Archive has been recording everything that aired on cable news television networks going back to June 2009, and it is all available to be viewed by anyone for free. The covered networks include all of cable news television (Fox News, MSNBC, CNN, CNBC, Fox Business, Bloomberg, CSPAN), plus the basic networks NBC, ABC, CBS, FOX and some others including international (BBC, Al Jazeera).
The video is only available to be viewed split up into 60 second clips, due to copyright reasons. Also, the video is not made available until 24 hours after it is aired. But it is good quality and can easily be downloaded using a browser extension such as Download Helper. And all spoken words are automatically transcribed and entered into a searchable database.