Maybe not "ultra severe" but definitely expect some important bottleneck.
I would settle for a lesser card like the Radeon 7770 or GeForce 650-Ti.
And since you have an old computer, why not looking for second hand cards? You might find great deals in your area, check on Kijiji, ebay, cragslist, etc... For instance, I recently bought a used 5670 for only 30$. If you want a little more power, you can probably find great deals on 6870 or 560, something like that.
For reference I run an e8400 @ 3.6Ghz which is a similar generation yet stronger cpu and I recently purchaced a 660GTX.
I find that in most games my cpu bottlenecks my gpu by around 50%, especially in source games and bf3 multiplayer (I expect mostly due to e8400 only being dual core and bf3/source scale well to quad cores).
I wouldn't recommend getting a 660/7870 unless you are planning to upgrade your cpu/mobo soon or else it will be a wasted purchace. I would do what the user above has advised if you need a new card.