Beta comes out in 2 days, there will be benchmarks then.
Based off the Alpha (which will be slightly different from the real thing), a 6870 gets 37 min and 48 average at 1080. This is on high quality. There will be an Ultra quality in the real thing as well.http://gamegpu.ru/Action-/-FPS-/-TPS/Battlefield-3-Alpha-test-GPU.html
Although things will change, you will probably be able to run it on High just fine.