The first questions I would have the Senators ask her involve the unamendable parts of the Constitution, as I have noted a couple times before. But the particular questions I would ask Kagan involve her love of Jane Austen. She allegedly rereads Pride and Prejudice every year. Will some educated Republican staffer know that Pride and Prejudice is not a treatise about affirmative action?
I would ask her about love, manners, vulgarity, censorship, and tyranny--the themes explored by Azar Nafisi in her wonderful novel, Reading Lolita in Tehran, which has a most insightful chapter on Austen--see my initial post and follow-up. In other words, force Kagan to make the case for civilization and explain what causes the coarsening of a culture--and its relationship to the rule of law. She might also opine why Tocqueville's notion of the legal profession as America's aristocracy is now something of a lawyer joke. The Republicans by and large muffed their chances with Sotomayor--they should have used her strengths against her, as I argued: e.g., force her to repudiate racial/ethnic preferences.
Proper questioning of Kagan will disperse this preposterous fluff about consensus-building (and ability to seduce Justice Kennedy), and we can get to the core problems, summed up in her defiance of federal law, as Bill elaborates below. The point here is not to defeat her--likely impossible short of some scandal--but to expose the man who nominated her and those who vote to confirm her as failed guardians of liberty who should be defeated.
ADDENDUM: Paul at Powerline notes that the three women Justices would come from three boroughs of New York.