You might be able to get away using that same power supply. If you check out the review for the
GTX 550 Ti, you'll see that it uses 262 watts at full load, and that's using a Core i7 920 @ 4.0Ghz, which uses a lot more power than your Athlon II X4 620 processor @ 2.60 Ghz.
Granted you don't want your power supply running continuously at 100% (around 70% would be good), but there should be enough headroom for you to be able to stick with the same power supply.
If it were my system and I was on a limited budget, I would give it a shot. If there were any errors or system instability, then I would spring for a new PSU.
Then again, a new PSU might bring you some peace of mind. The question is whether or not that's worth the $50 to you.