I laughed when I saw that the Obamas want a "rescue" Portuguese Water Dog. My mom got a Portuguese Water Dog (PWD, Portie) puppy a couple of years ago. They had to wait 6 months and sign an agreement that basically made them the caretakers of the dog, not the owners. They can't transfer the dog to anyone else without the breeders approval, they were required to spay her, required to take various veterinary care of her, etc. etc..
Portuguese Water Dogs are a boutique breed. My impression is there are no "backyard breeders" both because there is no demand and because breeders are very careful who they allow to have their dogs.
I don't think there are rescue Portuguese Water Dogs. You really have to want one and have thought about it in order to get a Portie. If the Obamas find one, my guess is it will come from an Obama supporter who suddenly finds they can't take care of their one or two year old Portie and gets permission from the breeder to let the Obamas "rescue" it.
If they really want rescue, I think they will end up with a Labradoodle or some other more popular breed.
Update: After I wrote this I found the link for the Portuguese Water Dog Club of America rescue
They say to try to contact the breeder first if you know of a dog in need of rescue. I'm guessing the rescue part of the club is not too busy....