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The Supreme Court signaled Wednesday that it might uphold a key element of Arizona's immigration law, as justices across the board suggested the state has a serious problem on its hands and should have some level of sovereignty to address illegal immigration.

The justices appeared ready to allow a provision requiring police officers to check the immigration status of people they think are in the U.S. illegally.

The justices strongly suggested Wednesday they are not buying the Obama administration's argument that the state exceeded its authority, with Chief Justice John Roberts at one point saying he doesn't think the federal government even wants to know how many illegal immigrants are in the country.