Websites aside, is it theoretically possible for the bitcoin-qt client to support some kind of 2nd factor authentication?
Yes/No. It does support two factor authentication: Thats what wallet encryption is, you're protected by knowledge of the password and possession of the wallet file.
But no, because control over your computer moots security provided only by your computer.
There are a number of hardware wallet devices coming out which outsource possession of private keys to USB dongles that require a button press to authorize a transaction... those will keep you safe even if your computer is compromised.
Hardware keys are definitely the way to go for anybody in this game - I have invested a lot of money for somebody with a family to raise in bitcoin as I could see the potential for the future and it was worth the gamble. I still believe in the concept, just clearly the security needs to be addressed.
This experience for me, whilst devastating, has taught me some interesting lessons and that is a positive I can take away from the whole thing.
Oh and if the bastard who stole my money ever reads this - you are forgiven for stealing my money. You are not forgiven for the pain you caused myself and more importantly my wife.