It looks like the demo needs more than 1gb of VRAM to run properly. I'd guess that with anything less than 1.5gb, you'll be bottlenecked by swapping data to and from the GPU (if it runs at all).
I added it up and the demo needs at least 950mb per frame of memory, and in the worst case it can actually use up to 1.5gb per frame depending on which debug options you enable.
If you're feeling adventurous and want to try building the demo for yourself, find "render_glsl.h" and change this line:
enum {giDim = 256};
to this:
enum {giDim = 128};
That will reduce the voxel resolution, cutting down on the quality but drastically reducing the memory requirements. Also, if you try this, re-download the demo from my site - I updated it so that it will build out of the box.