As Jonathan Adler notes, the Supreme Court has asked for the views of the United States in U.S. Chamber of Commerce v. Candelaria (cert petition), where the Chamber is challenging Arizona state law creating additional penalties on employers hiring illegal aliens. The Los Angeles Times posits that this puts Solicitor General Elena Kagan in the awkward position of alienating social conservatives (by siding with the Chamber) or alienating "Latinos, civil libertarians and the U.S. Chamber of Commerce, which sponsored the appeal to the high court" by siding with Arizona.
The Solicitor General's opinion is certainly important: as Cathy Sharkey notes, the Supreme Court has often sided with the Solicitor General's view of federal preemption. And it's perhaps true as a predictive matter that anyone unhappy with the SG's brief will blame or seek to blame Kagan. It's not entirely clear to me that that is fair, however. On a question with this much political significance, with legally colorable arguments on both sides, there are going to be a lot of stakeholders weighing in. The Attorney General's office is certainly going to want a say. Homeland Security head Janet Napolitano (who was both the governor who signed the law, and a supposed SCOTUS short-lister herself) will likely weigh in. The career staff in the SG's office will have input. And there is a president and a vice president who like to be hands on on legal issues. At the end of the day, Elena Kagan might be pretty far down on the list of people who are the "deciders" on this particular brief.