Display size doesn't matter; it's about resolution. Judging from these
two articles, maintaining a 60fps minimum on today's hardware is borderline impossible on the highest settings at 1080p. Crank the detail down a bit and you'll get it.
It looks like a 770 or 7970 is the minimum you'll want for at least 50fps, and it just goes up from there. If you want that 60fps, you'll need a SLI/Crossfire setup, at least 770s.