"We have two criteria that have to be reconciled. One is that Malia is allergic, so it has to be hypoallergenic," he said. "On the other hand, our preference would be to get a shelter dog, but a lot of shelter dogs are mutts like me."
Add to that the strain of the inevitable attention that comes to a cute pup in the White House. On Thursday, President Bush's normally docile Scottish terrier Barney bit a Reuters reporter on the right index finger.
So, how to choose?
No breeds are completely hypoallergenic. However, some breeds have a tendency to cause fewer problems - mostly those that don't shed and need to have their coats trimmed regularly, or those that tend to shed less, said Stephen Zawistowski, an executive vice president for the American Society for the Prevention of Cruelty to Animals.
Relatively common no-shed breeds include poodles, bichon frise, Portuguese water dogs and Maltese, but these breeds need professional grooming, which can be expensive. Other breeds that have a tendency to shed less are Schnauzers, Westies (West Highland white terriers) and Scottish terriers, Zawistowski says.
Purposely bred crosses like goldendoodles also have the no-shed coat, but random-bred mixes of dogs like poodles will also tend to have that coat, Zawistowski says.
The Obamas could adopt from either a shelter or a breed-specific rescue group. Gary Weitzman, director of the Washington Animal Rescue League, says that right now about a quarter of the 250 dogs in their shelter are purebred, but the number can be higher.
"In September we had 78 dachshunds - we'd just done a rescue from a dachshund puppy mill," he says.
An ideal first dog should also be good with kids and visitors.
One advantage to adopting an adult dog is that personality traits are fully developed and good temperament testing can help choose a dog that's suitably sociable.
If the kids insist on a puppy, it's harder to predict. Almost any breed of dog can do well with children if raised with them.
Stanley Coren, a psychologist who has written a series of best-selling books on dogs, recommends breeds including beagles, cocker spaniels, golden retrievers, Labrador retrievers and poodles for families. But whatever breed is chosen, a puppy will need intensive socialization.
"Start introducing it to what it's going to be dealing with around the household," says Zawistowski. That includes children, but dogs can also be afraid of anything - men with mustaches, people with hats - if they're not used to them, he notes. "Those Secret Service guys look intimidating even on television."
A new dog can be a daunting choice, especially when made in the spotlight. But it's worth it - and for more than just the kids.
"I'd like to know that President Obama has a dog," Zawistowski says. "When he has a bad day, what's better than having a dog walk over and say, 'Hey, things aren't so bad?"'