It might work, but it depends on what you have in your system and generally speaking it will be a long shot. Also, forget about running an overclocked card. Anything higher than stock clocks will push the power consumption too high for you to even a remote chance to run the card.
I've seen different things regarding what the GTX 460 requires for power consumption. If it takes 24amps on a single 12v rail then you will definitely not be able to power it with that PSU. I've also seen it stated that it needs 37amps combined on the 12v rail, which again, you will not be able to achieve.
Although your PSU has 2 rails at 18amps, which would be 36 and awfully close, the maximum combined output is almost always below that number. For your PSU it is only 26amps maximum combined output on the 12v rail. To find the maximum combined output you take the 312w shown on the bottom line of your PSU's power table and divide it by twelve.
So basically if you want to try it out, you can. However, I'd strongly recommend buying a new PSU as the odds are not at all in your favor.
It also has a rebate so the total price after $20 rebate is $44.99.
There are many other options, but this is just one that I've previously purchased and I'm familiar with. Some people swear by only buying Corsair or Antec PSU, however, if your budget does not allow such a purchase, the above item is a decent alternative in my opinion.
It has 2 12v rails at 25amps max each. Combined 12v output is 37amps. It is also quasi-modular. The only bad thing about it is that both 8 and 12 pin CPU cables are on the same cord, so one of them will always go unused, but, that is a minor annoyance.
There is also a higher wattage version of that Fatal1ty PSU, but, it's manufactured by a different company, so all the positive reviews for the 550w model can't be used to infer the higher wattage version is just as good.
Using the Guru3d website a GTX460 1gb model:
@ 765mhz - 815mhz requires a 550 watt PSU
@ 750mhz requires a 500 watt PSU
@ 725mhz requires a 450-500 watt PSU
Lower/stock speeds and 768mb models can work with 450 watts.
It also depends on your overall system power usage; extra drives, overclocking, etc.
You might be okay. Many good PSU's are perfectly capable of delivering more than their rated wattage. The Guru3d article I linked points out that they are running on a heavily stressed and overclocked machine, so your power requirements may be similar. I only suggested 850 watts to be on the absolute safe side. The only x-factor is your desire to push the cards to their maximum overclocked/overvolted limit, which usually increases power usage considerably. If you experience problems, just back down a bit.