From this:

(Attorney Kris Kobach) filed a lawsuit Monday challenging the validity of a 2006 Nebraska law that allows some illegal immigrants to pay in-state college tuition... The lawsuit names the University of Nebraska Board of Regents and other state college boards as defendants.

...[His earlier] attempt to challenge Kansas' in-state immigration tuition law in federal court fell flat, when the court determined that the plaintiffs - a group of students paying higher out-of-state tuition - hadn't proven they were harmed by the law.

In the Nebraska case, Kobach argues that residents' taxes are being used to support the state's immigration tuition law in violation of federal law.

The latter is similar to a case he's pursuing in California which was dismissed by a lower court but after appeal it was reinstated is now pending before the California Supreme Court.

While it would be great if he succeeds, the way to block laws like this right now is to discredit politicians over the fact that they're willing to take college educations away from U.S. citizens in order to give them to foreign citizens who are here illegally. See the DREAM Act summary for a question you can ask. If even just a few people asked questions like that on video in an attempt to have an impact on the careers of politicians, it would send a very strong message.