Sheri, I have used this service more than a couple of times for my kids. It has never taken more than 4-6 days, even though they say two weeks for expedited service. Like Fred said, the secret is the overnight mail thing.
Also, here in Maryland you can get a state "ID" card without having a license at the Motor Vehicles Administration's local office. But that requires a birth certificate, which can be gotten on the spot at the local health department.