SPOILERS ABOUT SEASON 4! At the end of season 4, the Doctor must erase Donna's mind because a human/ timelord hybrid can't exist. That said, wouldn't the human/timelord hybrid version of the Doctor die? I could totally see Rose making out with him on the beach and as soon as the real Doctor left, the hybrid would die. Hilariously tragic.
I think the problem is that Donna was originally a human so therefore a human body can't handle being part time lord but since the doctor number 2 was a timelord body it isn't much for it to handle a human existence inside it I mean like the ninth doctor said "how do you humans get around in those things?"
Basically as said above and mentioned in the episode. Its the same thing with a character later on, humans in Doctor Who can only handle so much information and memories without pain and still be human. Lazarus Experiment is a good episode that discusses this. Basically the thing in Dr.Who with humans is they are so limited by the physical, but their minds and wills are endless.