That sounds high to me... I just had a root canal myself and my "out-of-pocket" expense after my insurance is around $750.
Granted, it is still an INSANE amount of money!
Is this a dentist that you've been going to for awhile? I definitely agree with the suggestion to shop around and see what other dentists would charge... however, just be careful. You don't want to sacrifice great work just to save a little money - especially with something like a root canal.
Also, when I had mine done, since I didn't have an extra $750 lying around I applied for this thing called Care Credit - which is pretty much a credit card that you can use solely for medical/dental (and even veterinarian apparently) bills. I didn't like the idea at first but they gave me 18 months no interest so it really helped.
I believe it's a national program so I would think they'd have this available in Arizona...
Good luck :)