Well, in fairness to the First Lady, she wasn't the instigator of the charge, and didn't outright endorse it. Still, it is a ridiculous thing to have been asked and she should have said so - I doubt most of those objecting to Miers (on the right) would be upset had someone like Edith Jones or Janice Brown been nominated.
Elitism ("she's not an ivy leaguer", "not pretty enough" etc.) is more of what I've seen (from some).
Actually it was a WH spokesman whoe raised the allegations of elitism and sexism.