I'm not saying you should use a cheap PSU - I'm saying if you must, it will most likely be OK.
I now run the same setup using a Corsair HX-750 PSU. In the long run your better off with a good quality PSU, but if like me, you didn't have the money to upgrade both the GPU and PSU at the same time, you could always run it from your current one for now.
For the record, my Dell PSU never died, I replaced it simply because I was considering CF HD6870's as future upgrades, and because with the CPU overclocked, the voltage to the CPU had a bit too much fluctuation for my liking. It was fine when it wasn't running any overclock though. I've actually kept it as a spare for testing or emergency use.