Quoting pitbullprincess:" Here its a choice to recieve your childs card and since we have been moving so much I didnt want ... [snip!] ... all the time but clearly the us is getting smart about saving those tax dollars so I cant gripe just need to get my butt gear"
I've never heard about receiving it the same day, but I had mine sent to me automatically. When I went for my son's name change, it took about two weeks for them to mail it out. I don't know if they would issue you the card right then and there but they might since it is his first time ever receiving one.
As far as the BC goes, you can request a copy of it be sent to you. It's like $25 I think. Or if you still live near where you had him, you can go into the vital records office and pay for a copy of it and have it that day.