Supreme Court justices took a dim view of the Obama administration’s claim that it can stop Arizona from enforcing immigration laws, telling government lawyers during oral argument Wednesday that the state appears to want to push federal officials, not conflict with them.

The court was hearing arguments on Arizona’s immigration crackdown law, which requires police to check the immigration status of those they suspect are in the country illegally, and would also write new state penalties for illegal immigrants who try to apply for jobs.

The Obama administration has sued, arguing that those provisions conflict with the federal government’s role in setting immigration policy, but justices on both sides of the aisle struggled to understand that argument.

“It seems to me the federal government just doesn’t want to know who’s here illegally,” Chief Justice John G. Roberts Jr. said at one point.

The Arizona law requires all police to check with federal officials if they suspect someone is in the country illegally. The government argues that is OK when it’s on a limited basis, but said having a state mandate for all of its law enforcement is essentially a method of trying to force the federal government to change its priorities.

Solicitor General Donald B. Verrilli Jr. said the federal government has limited resources and should have the right to determine the extent of calls it gets about possible illegal immigrants.

“These decisions have to be made at the national level,” he said.

But even Democratic-appointed justices were uncertain of that.

“I’m terribly confused by your answer,” said Justice Sonia Sotomayor, who went on to say that the federal government can always decline to pick up illegal immigrants when Arizona officials call.

The Obama administration was on its firmest ground when it argued Arizona should not be allowed to impose state penalties such as jail time against illegal immigrants who try to seek jobs.

Federal law chiefly targets employers, not employees, and Mr. Verrilli said adding stiffer penalties at the state level is not coordination. He said Congress’s 1986 immigration law laying out legal penalties was meant to be a comprehensive scheme, and Congress left employees untouched — and Justice Sotomayor seemed to agree.

“It seems odd to think the federal government is deciding on employer sanctions and has unconsciously decided not to punish employees,” she told Paul D. Clement, who argued the case on behalf of Arizona.

A decision is expected before the end of the court’s term this summer.

Only eight justices were present for the arguments. Justice Elana 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.

Gov. Jan Brewer, who signed the measure into law, was present for the arguments, as were members of Congress who follow the immigration issue: Rep. Zoe Lofgren of California, the top Democrat on the House immigration subcommittee, and Rep. Steve King, an Iowa Republican who has fought for an immigration crackdown.

Critics have said the law, known as SB 1070, will lead to racial profiling of Hispanics in Arizona. But the Obama administration has not challenged the law on those grounds, instead focusing on issues of federal versus state power.

Mr. Verrilli said Arizona’s goal is to try to force the federal government to change its priorities, but he said those policies are designed at the national level in order to balance concerns over available resources and international relations.

“What [Arizona is] going to do is engage effectively in mass incarceration,” he said. “It poses a very serious risk of raising serious foreign relations problems.”

Some of the justices, including Justice Samuel A. Alito Jr., seemed concerned that allowing police to perform immigration checks could end up leading citizens being held even longer during stops by police.

Mr. Clement said the law still complies with the Fourth Amendment’s limits on unreasonable searches.

Anticipating an unfavorable ruling, Sen. Charles E. Schumer, a New York Democrat who is a critic of the Arizona law, said Tuesday that if the court does uphold the state’s law, he will introduce legislation to overturn that decision and grant the federal government sole control on immigration matters.

Mr. Schumer’s legislation would also overturn a 2011 Supreme Court case that upheld a separate Arizona law that requires all businesses in the state to check employees’ legal status using E-Verify, the federal government’s electronic verification system.

In that instance Congress specifically left open the chance for states to pass their own business licensing laws, and in a 5-3 ruling the justices upheld Arizona’s attempt.

Since Arizona passed its laws, other states have followed suit. Local enforcement laws have been adopted in a half-dozen states, though all have been challenged in court. Still states have adopted requirements that businesses use E-Verify.

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