I agree with Jason that there would be an idealistic, hopeful signal sent by having the Obama girls enroll in a DC public school. That said, I simply cannot imagine the Obama parents doing that--and not only because of security/privacy concerns.
Michelle and Barack are both hard-core strivers raised in modest, middle-class families that instilled in them the importance of getting the best education possible. Starting in the fifth grade, Barack attended Honolulu's Punahou School, a private college-prep school. Michelle, meanwhile, finished up her schooling at Chicago's Whitney Young, a highly selective (and today top-rated) public magnet school. He went on to Columbia (after a couple of years at Occidental), she to Princeton, and they both wound up at Harvard Law. These are two people for whom a top-notch education was clearly seen as a key element--arguably the key element--of success.
This is not to disparage all DC public schools, especially at the elementary level. But DCPS isn't exactly known for its excellence. As such, it would be something of an educational risk for the Obamas to have their daughters attend public school in the district. (Besides, one can only imagine the ruckus that would be raised on down the line if the Obama gals started off in a DC public elementary school only to transfer to a private school for middle school.)
So no matter how much the new First Parents would like to be good liberals and
support the notion of public schooling by sending their daughters to, say, Lafayette or Janney, can they really overcome that ingrained impulse to pick
the best school available to them? Doubtful.