I have had my two cats with my last 3 children. Neither here nor there for them. My female kitty loves my oldest daughter and will always choose to be with her. My male kitty loves me and sleeps next to me. He he fine if I lay with a baby, but once they become mobile he prefers to stay away until they learn to not pull hair. All cats are different!
You also wanna watch it because cats like milk and if ur baby is laying there and the baby smells like milk you dont know what could happen just be careful
We have two cats, and they both reacted very differently. Our male cat is generally very chill and affectionate. At first he was uncertain about this new little thing that smells different and makes weird noises, but now he likes to lay with me while I sit with the baby on the couch. He has also led me to the baby when he's crying, and if he can't lay with me, he takes up a guard position.
Our female cat has always been more nervous, and she was wide eyed and skittish when we first brought him home. She has calmed now, but she still disappears if he starts crying. She gets interested sometimes, but his sudden movements make her nervous. She did try to walk across him once when I was sitting on the couch with him, doing skin to skin. Luckily there was a blanket over us, so she didn't scratch him or anything.
Also, I don't let them in the nursery, because I don't want them in his crib. He sleeps in a bassinet in our room right now, and the cats get kicked out at night. Some cats will lay on the baby's face in the crib, so you have to be careful. Mine haven't made any move to do so, but the male likes to get as close to me as possible and has flopped down in my face before, so I'm not taking any chances.