I wouldn't say you actually "need" a new PSU for it. But I do warn that such a configuration could begin to stress that PSU should the CPU and GPU both have to operate at full load for extended periods.
Also, with better GPU's (5750/5770 & 6750/6770) within a $10 to $20 stone's throw of that 6670, it doesn't offer nearly the same performance/dollar value as a 5770. Especially considering how much better the performance of a 5770 would be.
If within budget, I'd be more inclined to go with the following card:http://www.newegg.com/Product/Product.aspx?Item=N82E16814121363
$110 ($90 after rebate)
To cover the additional power requirement, I'd choose one of the following PSUs:
Antec 380D for $40 - http://www.newegg.com/Product/Product.aspx?Item=N82E16817371033
Corsair CX430 for $45 ($25 after rebate) - http://www.newegg.com/Product/Product.aspx?Item=N82E16817139026
Basically, $50 more bucks (up-front) can get you a much better card and a high-quality PSU. If you go for the card and Corsair PSU, after-rebate cost is only $115, which is only $15 more than where you started with just the 6670 card.