One chart lists 750 watts as needed, but the chart is new and doesn't mention the cpu's used, or mobo's, etc., so I assume they are calculating for quad core cpus and up. The setup in question is using older, and perhaps less watt hungry parts. Is this why a 600 watt may be ok?
I'm going to say you can't. First, Aspire isn't very good. Second, the GTX470 needs two PCIe power plugs. Two in SLI mean you need four. It's hard to find a 650W unit that has that many, impossible (?) for a 600W. I''d upgrade to a bigger PSU.
Speaking of upgrading, I wouldn't run a slow dual core with two 470s. CPU bottleneck for most games I'd bet.