I think in the K affair, the Dems hurt themselves by dialing up the heat dial too far. The Pubs have done the same to themselves, time and again. Yes, I know, the base demands it. Sometimes the base, maybe more than sometimes, gets in the way of ultimate success.
I'm really not sure what else the Democrats could do. Another Clarence Thomas hearings situation reluctance wouldn't just pass nowadays.
Also, the Thomas' case contributed to what became known as "Year of the Woman" in 1993, which was greatly beneficial politically for the Democrats.