Over at Reason, Jacob Sullum is concerned:
As solicitor general, of course, Kagan has an obligation to defend federal laws against constitutional challenges. But her pro-censorship positions went beyond the call of duty. Together with some of her academic writings, her arguments in these cases provide grounds to worry that she will be even less inclined than Stevens, who has a mixed First Amendment record, to support freedom of speech.
Defending a 1999 federal ban on depictions of animal cruelty, Kagan boldly asked the Supreme Court to recognize a new category of speech that, along with such historical exceptions as defamation, incitement, and obscenity, is entirely outside the scope of the First Amendment. “Whether a given category of speech enjoys First Amendment protection,” she wrote, “depends upon a categorical balancing of the value of the speech against its societal costs.”
Writing for the 8-to-1 majority, Chief Justice John Roberts called this claim “startling and dangerous,” adding: “The First Amendment’s guarantee of free speech does not extend only to categories of speech that survive an ad hoc balancing of relative social costs and benefits. The First Amendment itself reflects a judgment by the American people that the benefits of its restrictions on the Government outweigh the costs. Our Constitution forecloses any attempt to revise that judgment simply on the basis that some speech is not worth it.”
Certainly, the Solicitor General’s handling of the Citizen’s United case — where the Deputy Solicitor General came out in favor of book banning before Kagan backtracked — is not encouraging either. And if you're interested, Sullum has more worthwhile remarks on Kagan's approach to free speech as it relates to campaign finance here.