Do you think it's possible to spoil a baby?

My son is 2 months old. I hold him pretty much all the time, and I talk to him and love on him. When I sit him down and he starts gettin a lil fussy I pick him back up. My grandma tells me that I'm spoiling him and that he needs to cry some. I feel bad letting him sit there and cry. I love holdin him and don't want to put him down. My doc says babies need to be held and loved and you can't spoil them by doing that. I agree. What do you think?