"We've given this guy a ton of support both personally and professionally and he is regulalry throwing it back in our face, sending lengthy woe is me emails and generally deflecting the blame onto anyone and everyone but him"

I think that kind of attitude hinders growth, innovation, loyalty, etc.

I agree that you catch more flies with honey and with pat on the back motivation. It seems as if GillianLyn has given the honey and the pats on the back
"We've given this guy a ton of support both personally and professionally "

How much time/money do you spend on a crappy employee?
Ans = none
Employees should have a good attitude then when walk in the door, they will make mistakes, they will need guidance but if they have a bad attitude you will never change that, its not fair to the other workers for you to waste company money and time trying to accomplish such a task.

You are not doing someone a favor by keeping them in a position in which they are failing and will not excel.

Fire them, you are most likely sending them to a better place where they will fit in and succeed at what they are doing. Your workplace is not necessarily the right place for everyone, neither is it a kindergarden or daycare. (unless you are in the daycare business )

Right now Mr woe is me is stealing space and salary from somebody who could quite possibly be the best employee you ever hired.