No, you won't be able to run on Ultra at 60 fps. But you should be able to stay above 30. If this build is primarily for gaming, I'd recommend getting the phenom x4 965 instead of the FX 6300.
Try this...PCPartPicker part list
/ Price breakdown by merchant
/ BenchmarksCPU: AMD Phenom II X4 965 Black 3.4GHz Quad-Core Processor
($89.99 @ NCIX US) Motherboard: ASRock 970 Extreme3 ATX AM3+ Motherboard
($69.99 @ Newegg) Memory: Kingston Blu 8GB (2 x 4GB) DDR3-1600 Memory
($29.99 @ Amazon) Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive
($64.99 @ NCIX US) Video Card: HIS Radeon HD 7870 2GB Video Card
($204.99 @ Newegg) Case: Cooler Master Elite 430 ATX Mid Tower Case
($41.98 @ Amazon) Power Supply: Antec Neo Eco 620W 80 PLUS Certified ATX12V / EPS12V Power Supply
($29.99 @ Newegg) Optical Drive: Lite-On iHAS124-04 DVD/CD Writer
($17.89 @ Outlet PC) Total:
$549.81(Prices include shipping, taxes, and discounts when available.)(Generated by PCPartPicker 2012-12-18 01:35 EST-0500)
I was actually able to squeeze in a HD 7870 which should put you much closer to that "High/Ultra at 60 fps" mark.
If you have the extra cash, throw in a decent CPU cooler such as the Coolermaster Hyper 212 Evo.
And if you have any questions, don't hesitate to ask. I hope this helps; good luck!