I suggest you contact Asus directly. This desktop model has a 350W PSU and can come with a 6.5" GPU, such as HD8350. However, most 660s are around 9.5" That's much longer then the one you might have. Also, most systems with a 660 require a minimum of 430W. You might get by with 400W, but 350W seems too low.
Have you thought about removing the components and putting them into a bigger case with a larger PSU?