In some games that's just not possible (Metro 2033, Crysis 2 Ultra, Witcher 2 with Uber Sampling, BF3 multiplayer with 4xMSAA). Also, at low resolution such as 720P, the CPU becomes a critical factor in trying to get 60 fps minimum.
What is your CPU and clock speed? Do you plan to overclock the CPU or GPU?
Take a look at
this review to get an idea of the GPU performance in many games. There aren't minimums but looking at the averages can also help you.
I don't want to recommend you get a $300 card for a 720P display though since at that point I think it's worth it to get a new monitor first. I think HD7850 + manual overclock to 1.1+ ghz is a good mid-range card under $240. You may want to wait another 2 weeks before GTX660/660Ti launch to see if there are possible price drops. HD7850/7870 and 7950 are pretty much the best cards in the $210-320 price range right now. Otherwise you are looking at GTX560/HD6870 which are good for older games but probably won't get you 60 fps minimum in newer games even at 720P.