If you're looking to maintain the Responsive Web Design principles, simply applying position:fixed won't do the trick. If you want it to work nicely on smaller screens, you'll have to have conditional code. It'll have to be fixed on a "normal" screen, and you'll need to remove the class when the screen gets "too small". You'll also have to decide what "normal" and "too small" mean for you. See here for an example:
http://home.edgemontgeek.com/dev/stackoverflow/14919523/
Keep in mind that you'll also need to control for screen height. If the window isn't big enough to fit the fixed content, they won't be able to see it. You could consider having two columns that can be scrolled separately.