gtx 560 should work fine, i run a gtx 570 on ultra with no problems.
Disregard this. A 570 on full ultra settings but with 0x MSAA (meaning not true ultra) bottoms at 54 fps. It's largely ok, but it does have problems and goes below 60 fps in certain areas on several maps.
OP, a 560 should be fine to run the game on High settings, with post processing enabled but 0x MSAA enabled. The game will look nice and should rarely go much below 60 fps. If it does, and if that bothers you (as it probably should and will), you can always try dropping shadows down a notch for instance. In general, if you're on a tight budget yes those two components can handle BF3. I would really recommend that you get at least a 560ti or 6950 though. They cost a fair bit more than the price on that 560, but in general they are considered the true entry-level cards for gaming at 1080 in BF3 with high settings and never* going below 60 fps. Just a recommendation, nothing concrete.