Our older cat (5 year old neutered male) started doing this when we moved to a new house a few years ago. Only it wasn't spraying, but rather peeing on my bed, to the point that it would have soaked the mattress if I didn't have a mattress pad on. Yuck. I took him to the vet, who found nothing physically wrong. So, he became an outdoor cat! (It was either that or the SPCA, we were at our wits' end since he did this several times.) We are all much happier with him outdoors, and he has turned into a ferocious mouser! It has been about 2 years now and he knows he isn't allowed in the house. He has a cat door leading into our laundry room so he can get out of extreme hot or cold weather, and we keep his food and water in there. He will come right up to the laundry room door but he will not step into the hallway since he knows he will get in trouble if he does.
I do think it's worth taking your cat to the vet just to be sure there is nothing wrong, but be aware that he may be reacting to the stress of the new baby. Our kitten (a spayed female) sprayed my daughter's backpack a few months ago, and we caught her in the act and put her outside for 24 hours. She stood at the back door peeking in the whole time yowling, but we didn't let her in. Finally after her day of punishment was over, we let her back in and she has not done it since. But I think the key was catching her in the act so she could understand why she was being punished.
Good luck. Our animal friends have such socially unacceptable ways of telling us what's going on with them... =)