I'm probably late, but doing 1080p @60 fps DEFINITELY requires 4x the power that 720p @30 fps needs. BigMack is absolutely right on that account.
A very different thing is that when running low resolutions some other parts (95% of times the CPU or DirectX draw calls...) become the bottleneck and hence you don't see 4x the performance at the lower resolution.
But magic does not happen on computing. If performance moving to higher res is not linear is because graphics cards have power to spare and because of that they do a better work at the higher res. On lower res or with low settings GPU resources stay unnused.