I do parrot rescue along with the training business and believe that you can manage with the bird and the baby just fine. I have several birds including a cockatoo so if you want to see a bird who wants to have attention then just meet her. She has learnt that she will not get constant attention but she does get some and she goes with us when we go away or go camping. I also have 3 dogs,ferrets and 2 kids.
Believe it or not a new born sleeps a lot of the time so you will actually have plenty of time for the bird and someone else has mentioned as long as your bird is kept in the room that most of the activity in the house happens and he/she has a good rotation of toys the bird will be just fine.