In fact, from a conservative's perspective, the choice could have been much, much worse. Judging from conservatives who are now professors at Harvard Law School, Kagan did a great and "apolitical" job in a role where left-wing grandstanding goes completely unpunished. Unlike many in her milieu (and, I would suspect, colleagues like Sonia Sotomayor) she has treated conservative ideas with genuine intellectual respect and fair-mindedness.
On the Court, I would suspect that she will be a reliable (though not necessarily predictable) liberal vote (it seems that no one ever "grows" to the right after ascending to the Court) -- but then again, what do conservatives expect when a lefty like Obama is doing the nominating?
Her lack of a paper trail offers few clues about how she'll ultimately turn out, which of course makes the left nervous and complicates any effort on the right to oppose her. Indeed, let's hope those of us on the right use this occasion -- not to engage in gratuitous and ugly attacks on Kagan personally -- but rather to promote our view of why it matters that judges stick to their constitutional role of adjudicating, rather than legislating from the bench.
The fact is that Kagan is too savvy to have a "wise Latina" moment -- a remark that conservatives can use to showcase the objectionable biases in a potential Supreme Court justice. During the hearings (and with Court nominees, except in rare cases like Sotomayor, it's impossible to predict exactly what will happen afterwards) Kagan will seem reasonable, moderate, smart and good-humored. Her obvious intelligence and affability and likelihood to say nothing of import will put her opponents on the defensive -- and create the risk that attacks on her will seem mean-spirited and substance-free.
Again, perhaps that creates an opportunity for Republicans -- not to block Kagan (and then, in all likelihood, end up with a nominee that's no further right) -- but rather to continue to explain to the American people why our vision of jurisprudence is superior to the left-wing, "living Constitution" brand that would effectively transform justices into oligarchs, able to read their own political preferences into America's founding documents.