I like both cats and dogs, but I don't think a feline choice would have worked. Cats are aloof and have standards. What the Obamas like is the mindless adoration they get from their voters, and the right dog comes much closer to matching that tone than any cat ever could (a dog is a little too smart, but at least it will provide the slobbering worship that Barack craves).
Yeah, a cat would not blindly obey.