Watts are amps multiplied by volts. This being said, a 450W PSU would be equivalent to 37.5 Amps for the 12V rail. This is more than enough to handle a single GPU as long as it isn't a high end 68XX or higher one. I would opt for around 600W to go with the higher end cards, but as I mentioned a few posts up, replacing the GPU isn't really a good option unless you replace the motherboard, CPU and Ram.
Note that some PSU makers claim higher wattage by putting more amps to lower than 12V rail, which is kind of cheat to get more wattage, it is generally known that wattage is misleading and one should check that he has enough amperage for all rails individually. Also 12V rail is usually no more than 20A because of safety reasons, so 12V rail is split to several, which can complicate things further.
At one point there was bit of issues, when there was need to get more than 20A from single 12V rail and new PSU did not deliver more than 20A to 12V, however back then extra power connector was not possible to connect, so it had some dangers, but today I think all gfx card makers are getting it right.
Also as OP's machine is already those that require more of 12V than those of lower voltages, it will be important to make sure PSU one is buying is not one of those that put more amps to lower voltage rails to 'boost' wattage readings.
When choosing PSU I like to refer this page, I like my pc silent and more noise means psu heats more and wastes electricity or is too weak, well generally so, many exceptions are to that rule:
http://www.silentpcreview.com/Recommended_PSUs
Even thread is old, it has still working link to calculator and some good information of subject, electricity is not getting old with computers:
http://www.computing.net/answers/hardware/enough-power-supply/26032.html
Good thing with Core2 Duo is that it is taking quite little power, I have E6750 with 8800GTS and I think my PSU is 385W (I bought it at 2006 can't remember that far), it is under 400W for sure, but it has enough amperage because it has less amperage to lower voltage rails and more to 12V, I did buy PSU when I still worked as Computer technician, soon need to get new one as PSU output decreases with age, so it is now perhaps 75-80% of what it was at new.
There is just lot more things to consider than just Wattage when choosing PSU, I usually don't even look at wattage as it is just a selling point as is Megapixels with digital cameras, they don't tell anything about how good camera really is.