The only way I know will require a bit of work. Do you use Internet Explorer or Mozilla Firefox, or something else? The only way I know how to do this is with Mozilla Firefox, which is free so it couldn't hurt to install it and at least try it out (It's like IE but much better). If you don't have Firefox, here's a link:
http://www.mozilla.com/en-US/firefox/
What you want to do is download this download helper (it only works with Firefox unfortunately):
https://addons.mozilla.org/en-US/firefox/addon/3006
It might ask you to restart Firefox, or take you to a new page saying it successfully installed or something like that. Basically it will add this rotating icon at the far right side of the URL bar. It is 3 rotating circles (red, blue, yellow). What you want to do is load the video up on CNN, then click on the arrow to the right of this rotating icon. You will see a drop box drop down, and you will want to click on the middle icon that is gb .liberty.in.peril.gun.ban.cnn_576x324_dl.flv Then it will ask you where to save. Just choose a place and your download will start. Here's a pic to illustrate what I'm talking about:
Make sure you click the one I have highlighted. The one with the same file name above it, but the different icon won't work for me so I'm not sure what that one is.
This method works for most videos like this on most websites like Youtube, Google Video, etc. Also, just fyi, these files (including this particular one) are typically .flv files so you will most likely need to download a separate player for them unfortunately (lots of hoops to jump through this process isn't there!). Here's one I use and it works well:
Link
Please let me know if you have any questions.