Honestly, if there's any one avenue of game development where I'd recommend against getting a degree in, it's Game Design (okay, that and QA). As it was mentioned above, designers are like artists in that portfolio is everything.
I got my break in the industry as a designer by first working as a community manager; unless you've got a solid portfolio of work, no one is going to hire you directly from school as a game designer (well, you
could probably get into a few social gaming shops, but I dont know how long that path will stay open).
If you want to become a game designer, make games. Learn a secondary dev skill, whether it's code, art, whatever, and join forces with another who's skilled in the areas you lack, and just make something. I'd recommend starting with tiny game jam style games, projects that you can bang out in a weekend or two. Get a handful of those under your belt, and go from there.
Don't be too ambitious with your first games. Hell, clone asteroids.
Read design documents to get a feel for what's required in a larger scale title. Here's a good resource for that:
http://www.gamepitches.com/game-designs/In the meantime, keep learning. Study design on the side, but don't be afraid to explore other avenues in your schooling. You'll be surprised at what will help you as a designer down the road.