I know this is a semi-old post, but I'd just like to point out that 650W is absolutely plenty for a typical system with a single GTX 670. If your CPU and other components aren't too power-hungry, you can run two GTX 670s on it as well.
Always assuming the 650W PSU is actually any good. Fake wattages do happen.
Do you have any ideas about my problem? I've used the exact setup you suggested, 670 aside, and honestly can't see what's causing this issue..