I just tested mine at 1080p Ultra settings and 4x MSAA and got under 1200 so I'm not really seeing the problem on my end.
The only game where I've run into 2GB VRAM limitation so far was Crysis 3 on Very High settings + Very High textures and this was in 2560x1440 with any above 2x anti-aliasing method.
2GB is plenty of VRAM for 1080p gaming. Should you find yourself in a spot where you needed more than that, you'd need to tone down your settings anyway because your GPU could no longer cope with it anyway. So do yourself a favor; get the GTX 770, turn down your MSAA to 4x and stop fretting about the video memory limitations.