I would say no. Although the gtx 660 isn't a huge power consumer, a 450w would just be cutting it. (nvidia recommends at least a 450w)
Your computer is fairly good, your processor and video card are decently future proof.
This being said, if you ever felt like upgrading your GPU down the road, (like the maxwell, or keplar refresh 700 series) you would be stuck buying a better psu anyway.
I would suggest a good quality/good brand psu, as a faulty psu could fry your whole system and leave you with nothing.
heres a good quality 500w psu for only 39.99 after rebate: http://www.newegg.com/Product/Product.aspx?Item=N82E16817139027
This would work for you now, and a future upgrade most likely. If you ever wanted to go SLI with you gpu (rather than upgrading to another single card) perhaps a 600w psu would be beneficial: http://www.newegg.com/Product/Product.aspx?Item=N82E16817139028
59.99 after rebate