I fixed it by uninstalling New Vegas and Steam (I could have probably just uninstalled the game, but I wanted to be 100% certain), getting all my video drivers and settings properly tweaked (including the newest version of DirectX), and reinstalling. As you can see from the picture above, poor Doc Mitchell was the first victim.
Unfortunately, I installed both Steam and New Vegas before I finished tweaking my video drivers which resulted in some very bizarre purple/pink textures or shaders. The first game I decided to play after building a new gaming PC was Fallout: New Vegas.