GayPatriot expresses one view (thanks to InstaPundit for the pointer); Rosa Brooks at Slate's XX Factor and Christopher Beam at Slate also opine, with Brooks faulting Clinton for her (relative) silence.
Here's my quick off-the-cuff thought: There's something very sad about Spitzer's downfall -- an intelligent and successful man undone by his appetites, a lifetime of ambition and fighting largely squandered for a few moments of pleasure.
Those who disapprove of Spitzer on various grounds may well feel some vindication and schadenfreude, and they may be right to some extent. (I haven't followed Spitzer's career closely, but my guess is that I'd share their condemnation of much that Spitzer has done.) But surely one can't expect most liberal or liberalish Democrats, including both Hillary and Hillary's base, to feel that way. To them this is a sad occasion, the ruin of a man with whom they may have worked, and whom they likely respect in considerable measure (even if they have had difficulties with him, as Hillary has).
It thus seems to me that Spitzer's political allies might feel, both as a matter of kindness and of loyalty, that they should keep quiet rather than condemning Spitzer, or using his fall as occasion for some broader substantive discussion (for instance, "about what it's like to be a woman in a world where too many of her male peers think sex is a perk of the job"). If it emerges that Spitzer wants to continue in office in spite of his actions, then I think at some point fellow Democrats should speak out against him. But it looks like he's already being punished enough. I can certainly see why his allies might not want to pile on, and might not want to be seen by others as piling on.
On top of that, my sense is that Hillary has an extra problem: Any substantive statements she makes on this topic seem likely to play into the common public image of her as schoolmarmish and scolding. Yet another reason, I think, for her to stay as silent as possible.
Now there may well be other reasons as well, such as those mentioned by GayPatriot. My point is simply that there are so many reasons that it's hard to identify any as the main one -- and hard to condemn Hillary for doing what seems to be the more loyal and kind as well as the more politically savvy thing to do.