I wasn't at the Hillary event Noam mentioned below. And if Ben Smith says she choked up, I'm certain it seemed that way in the room. But having just seen footage on TV I highly doubt this is going to play out as some Ed Muskie moment. There was a real vulnerability to Hillary's voice, no doubt, but it probably wasn't enough for a full viral YouTube effect. (And I agree with Noam that, to the extent she seemed emotional, it was sympathetic. Although who knows what damaging gender-stereotypes it could accentuate, especially among male voters. After all, the only word Hillary's campaign invokes more than "experience" and "change" is "strength.")
P.S. Having been prompted by a question in part about her hair, Hillary's moment reminded me of an oodball experience: Yesterday I did a quick segment on Fox News. This involved the always-emasculating experience of someone applying heavy makeup to my face. But my charming makeup artist assured me I was in good hands. It turns out, you see, that the woman applying foundation to my rosy cheeks is also Hillary's designated pre-debate powderer. She explained that Hillary loved the job she did before one summer debate in New Hampshire that she's specifically requested her for every debate since--I think she said she's made her up eleven times now--and even flies her to out-of-state events. (About which I am making no judgments--honestly: I'd obsess over makeup too if I was debating in front of millions of people!--just one of those weird campaign-trail moments.)
Incidentally, I asked my beautifier whether Hillary is a basket case in those final pre-debate moments. She insisted not, and said that that sitting in the makeup chair seems to be one of the few moments of zenlike peace the candidates ever get.