From what little I've read about her so far, it appears that she has a scant record of written opinions for a Harvard Law School dean and is not progressively ideological enough (i.e. on executive power) for some on the political left but after listening to the first day of right-wing talk radio following the announcement of her nomination I think Dave Weigel of The Washington Post hits the nail on the head:
We're already seeing a line of criticism develop. If I can sum it up in the bluntest possible language, Kagan is a New York, Ivy League elitist, a critic of the military during wartime, who was picked because President Obama is all of those things.This is pretty much what I've been hearing out there and right-wing talk radio doesn't form Republican opinion and policy so much as it just serves as a vast echo chamber for it. I would expect to hear a lot of this narrative over the next few months but I also predict that she will ultimately become (possibly the first homosexual) Supreme Court Justice.