With the 6670 taking at MOST 60 watts, as long as the power supply is a GOOD one it should work fine.http://www.techpowerup.com/reviews/AMD/HD_6670/20.html
If you can get info on the power supply such as the 12 volt amp rating(combined if it has more then one rail. Also you can not ADD rails they should have a combined listing for just the 12 volt ones.).
IMAGE example. BTW, I run a GTX 650 ti on that power supply
I am NOT telling people to go out and use a 300 watt power supply to run a 650 ti, just it is all about what else is in the system.