Obama's choice of the current Solicitor General to replace justice Stevens on the Supreme Court is getting mixed reviews from progressives. Many were hoping for a bolder choice of a real progressive. Kagan is considered to be a moderate on many issues and perhaps conservative on issues like executive power. It is feared that anything less than a strong progressive would move the Court to the right.
LGBT activists are somewhat more supportive, though no one knows for certain if she will be a strong advocate for LGBT civil rights. She did oppose military recruitment as Dean of Harvard because of the military's discrimination policies against gays and lesbians. There is even some speculation that Kagan may be a lesbian, leading some gay activists to call for her to come out openly if she is gay, which could further complicate her confirmation.
The problem is that Kagan does not have much of a public record or written history for opponents or supporters to analyze. She has no judicial experience or written opinions to scrutinize. So far, the only thing right-wing opponents have come up with his her undergraduate thesis on the history of the Socialist Party, which seems to blame infighting among socialists for the demise of the SP in the United States.