my current system specs:
Motherboard: Asus M4A88t-M USB3
CPU: AMD Phenom II x2 560 black edition (with cpu cooler hyper tx3 evo)
VGA: Integrated ATI HD 4250
Ram: 4GB @1333 Mhz
HDD: 1 Western Digital 750GB
DVDRW: 1 Sony
Case: cooler master elite 310 with a 400w standard power supply
You shoudn't have any problems since the 6670 is a low power card, and newegg.com states that it need a minimum of a 400 watt PSU. I know people who used that card with a 300 watt PSU and didn't have problems.
I know the price is good but I would not use that psu in any of my builds. It's obviously an old design with poor efficiency. Stick with a quality power supply. PSUs have been discussed many many time at Tom's.