Interestingly, one of the few things we do know with some degree of confidence is that she has stated quite clearly that she believes there is no Constitutional right to marriage equality, and, unless she changes her mind for some reason, will form a solid fifth vote against marriage rights. (More here.) So queers' lives can continue to be kicked around for another couple of decades or so.
There won't be any significant opposition. The fundamentalist right is already declaring her a Sekrit Lesbian and has further declared that no fag is fit for the Court, in pretty much those words. This is predictable, but worse, also strongly discourages any non-rightist opposition. (The neoconservatives like what little of their record is available, so are opposing but not with vigour.) Mind you, there wouldn't be much left opposition, because the left - such as it is - can be consistently counted upon to fold like a cheap accordion. Myers didn't get on the Court because the "right" had a fit. Kagan will, because the "left" won't, and Mr. Obama knows it.
So unless the right can uncover something, she's who we get. It's hard to say what she'll actually do once on the court, because, well, we got nothin' much to find out. She's a cipher; she's strenuously avoided anything beyond ambiguity and manoeuvring space when she's had these questions thrown at her, for a long time.
Except when it comes to marriage equality. We do know where she stands there.