It will cut it yes, as your cpu isnt that higher power and you dont have loads of additional hard drives and stuff to power as well.
I personally wouldnt run anything less than a 500w psu if i had a graphics card that didnt only take power from the pcie slot, but that's just me.
If you've already bought the psu, then dont worry about it, it'll work fine.
If you havent, look to upgrade to a slightly higher wattage if you can.
Also, what brand psu is it?