Jonathan Bernstein's read:
The real thing Kagan -- and Obama -- need to persuade Kennedy to do is to consider retiring with a Democrat in the White House. For that, it really might pay to avoid a "a full-throated counterweight to the court’s conservative leader, Justice Antonin Scalia." Kennedy will turn 74 this summer. I've always said that it's a mug's game to make predictions about politicians and retirements, and that must be even more true about Justices on the Supreme Court. I would say, however, that if he considers retiring over the next several years, and if he cares about what happens to the Court after he's gone...well, if those things are true, then it's pretty easy to imagine the incentives involved and how Obama's nominees change those incentives. We can assume that Kennedy would prefer to be replaced by someone similar to himself, and then guess at where he perceives the next Democratic and the next Republican appointments would be. Presumably, given his voting pattern, he'd prefer to be replaced by a Republican appointee -- but relatively moderate picks by Democrats might close that gap somewhat (as might extremist rhetoric from Republican candidates).
This assumes that Kagan is a moderate. But we have no idea whatever what she believes, because she has managed to live a life with no apparent public beliefs. I suspect she's actually very liberal. Why else the long radio silence on everything - along with exquisite careerist strategizing?