Ok... I'm not sure if I understand this right, but from what I read, I am assuming the child is yours and not your fiances. If I'm wrong about that, then disregard this. I am the mother of a 10 month old baby girl, and I have been dating a man who is not my daughter's father since she was about 1 month old.(although he didn't meet her until she was 3 months old) My philosophy with his relationship with my daughter is that she is not his daughter, and so I can't expect him to do anything for her. I never asked him to do anything until he first suggested it himself. This way he never felt like I was trying to force him to be a father to my daughter. But, as time has gone on they have bonded. He still doesn't change diapers (He wakes me up or lets me know so I can do it, but hey like I said, it's not his daughter), but now he gets up with her in the morning and feeds her so that I can sleep in, he puts her to sleep, he plays with her, and he almost always wants to carry her and hold her whenever we're out together. Now, I have no problem saying "Can you watch her while I shower" or "do you mind giving her a bottle" or whatever, because they are things that I know he feels comfortable doing.
Another thing, and this may apply even if Nick is the father of the child (again, I was unclear in reading your message) one thing that I noticed is that my boyfriend didn't seem to feel as comfortable with my daughter until she got a little bit older. A lot of men are unsure around really young babies. They relate better to children that they can play with. So, as my daughter's personality started to develop and she became more interactive, my boyfriend became more enamoured with her. Now when we see each other, he'll often say hello and pick up my daughter before kissing me hello, and he always asks how "his" baby is when he calls.
I don't know if I articulated that right, but I have read that a lot of men don't know how to handle newborns because they aren't as interactive as older children. Once the baby appears to be a little more sturdy and a little less fragile he may warm up.
But, I do want to stress, that (this again is assuming he is not your fiance's son) it's important to let your fiance know you are a package deal. While, I said I never expected anything out of my boyfriend. I did want him to respect my daughter and treat her friendly. My daughter already has a father, the relationship she is forming with my boyfriend is a unique relationship. And while he may be a father figure to her in coming years, I will let them determine the depths of that relationship.
I don't know if this was any help or makes any sense to you. I hope it does.