Buying a prebuilt gamer for $600 is a tall order. If you built it yourself you can take advantage of cherry picking components on sale and have good deals. Also, you aren't paying another companies costs to build it. You could find a good future gamer candidate that would need a PSU and Video card upgrade later, that would run about $600. However, a system with a good video card is going to be tough.
This is probably the best one I could fine that would play some games on lower settings, but it has bad reviews. http://www.newegg.com/Product/Product.aspx?Item=N82E16883227443