These are twin Yorkies (Yorkshire Terriers) named Toby and Chloe. I'm not sure which is which.
Yorkshire Terriers are a long-haired breed - but don't shed! They have hair (as opposed to fur) that grows continuously which means they need to go to the doggie beauty parlor every six weeks or so. Yorkies carry less dander on their coat; don't usually have that "wet dog" smell when caught in the rain; and, are a good choice for people with dog-related allergies.
They would be a perfect choice for the Obamas!