In fact, I'd bet at least one Dem will explain his/her vote against confirmation something like this: "Although sexism might play a part in why some of my 'friends' across the aisle object to Ms. Miers, my own concerns are [blah, blah, blah, blah]. Therefore, I cannot in good conscience vote to confirm a nominee who might roll back [blah, blah, blah], take us back to [blah, blah, blah], and erode the civil liberties that [blah, blah, blah, blah]."
And should it, it'll kinda put a dent into the Dem's usual, and future, "promote" women as a sex kind of stuff. Their "for character" while slamming "sexism in the Repub Wing", could backfire in future "staging events". Time will tell. If they do this, it could be hell on their "female" quota usual platform.