Well, I have a 6870 (1 GB) and I've never, as far as I know, ran into VRAM Issues at 1080p even when using MSAA and the such. When playing on Ultra the framerates in BF3 are, obviously, way too low, but it its a consistent frame rate and doesnt seem to stutter or grind to a halt in the way at least I would expect it would if you're running out of VRAM. So, what i gather, and I may be wrong know, and correct me if I am, but it seems like the GPU can flush out resources its not using, at least to some extent, to keep the VRAM buffer in check.
However, if you REALLY do need 3GB of buffer than jeez... but pushing boundaries will move tech forward.