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A decision is expected before the end of the court’s term in June.

Just eight justices were present for the arguments. Justice Elena Kagan recused herself from the case, presumably because she was the Obama administration’s solicitor general in 2010, when the law was being debated in Arizona.

In one pointed exchange, Justice Antonin Scalia said Arizona’s law doesn’t target anyone the federal government hasn’t already decided shouldn’t be in the U.S.

He said the administration is trying to force Arizona to heel to the administration’s own priorities — in which Mr. Obama has called for deporting some categories of illegal immigrants while leaving others untouched — rather than to what U.S. law actually says.

He repeatedly peppered Mr. Verrilli with questions about whether there was another example where the courts had deferred to an administration’s priorities rather than the law.

“I think that’s an extraordinary basis for saying that the state is pre-empted,” Justice Scalia said. “It’s not criminalizing anything that isn’t criminal under federal law.”

Mr. Verrilli struggled to come up with an answer but said the state’s intent behind the law was the problem.

“The point of this provision is to drive unlawfully present people out of the state of Arizona,” he said.

On that he got no argument from Cochise County Sheriff Larry A. Dever, whose jurisdiction includes 83 miles of U.S.-Mexico border. Speaking to The Washington Times after attending the oral arguments, Sheriff Dever said the reason illegal immigration is swamping Arizona now is because federal government policies pushed it away from California and Texas and into his state in the 1990s.

He said S.B. 1070 doesn’t have a major impact on his county — the county is close enough to the border that it already can turn over illegal immigrants to the U.S. Border Patrol for removal — but he said counties farther north will clamp down, which should relieve the flow of people crossing through his county.

“It was moved elsewhere, from San Diego and El Paso, into southern Arizona. The reason it moves elsewhere is because it can,” he said. “That’s our whole argument. We want the federal government to take up the cause and have the resources it needs to keep it from moving from one place to another.”

Sheriff Dever said Homeland Security officials invite state and local police cooperation in every area of anti-terrorism enforcement except immigration law.

“Why is that?” he asked, adding that the same smugglers who guide people across the border also traffic in drugs and could potentially aid terrorists.