The recommended listing is quite a bit over what is required, simply b/c the companies cannot afford to have people with way underpowered rigs buying the card and then complaining. If they don't state [a slightly bogus] power requirement, than they'd be filling out refunds left and right.
Just look up the TDP (total dissipation power) of that card on a specs site, that is the max it'll draw under load.
Then use a PSU calculator to see how much your /current/ system requires. If your current system + TDP is less than your wattage, you should be good.
There are other factors involved (amps on the +12v being a major part of it) but that all depends on the build quality/manufacturer of your PSU)
I'd say go ahead and install your card, it shouldn't hurt much (well it has a slight chance at killing the PSU but you're replacing that anyways) ... at most your computer will just shutdown if it can't handle the load