During the 70-minute arguments, Clement faced relatively little tough questioning from left-leaning members of the bench.

"There will be a significant number of people who will be detained at the stop, or in prison, for a significantly longer period of time" if the state law is allowed to be enforced, warned Justice Stephen Breyer.

Justice Ruth Bader Ginsburg said the provision on carrying registration is especially problematic. "Congress enacted a complete registration scheme which the states cannot complement or impose even auxiliary regulations," she said. "We want the registration scheme to be wholly federal."

But the consistently tough questions were aimed at Verrilli from conservative members of the high court.

Even before the solicitor general began speaking midway through the argument, Chief Justice John Roberts framed the debate away from what has become a major complaint about the law: that it would target mostly Hispanic people for scrutiny and detention.

"I'd like to clear up at the outset what it's not about," Roberts said. "No part of your argument has to do with racial or ethnic profiling, does it?" Verrilli readily agreed.

Later the chief justice raised more serious concerns. When enforcing other law, "the person is already stopped for some other reason. He's stopped for going 60 in a 20 (mph zone). He's stopped for drunk driving. So that decision to stop the individual has nothing to do with immigration law at all. All that has to do with immigration law is whether or not they can ask the federal government to find out if this person is illegal or not, and then leave it up to you," Roberts said to Verrilli. "It seems to me that the federal government just doesn't want to know who is here illegally or not."

Justice Anthony Kennedy echoed the thought, suggesting the federal government is not doing enough on illegal immigration, which might give states discretion to intervene. Suppose, he offered, "the state of Arizona has a massive emergency with social disruption, economic disruption, residents leaving the state because of a flood of immigrants. Let's just assume those two things. Does that give the state of Arizona any powers or authority or legitimate concerns that any other state wouldn't have?"

Kennedy was echoing what the state had long been arguing, and he later suggested there is such authority.

Verrilli argued the law would hurt Washington's ability to carry out diplomatic relations with other nations, noting, "We have very significant issues on the border with Mexico."

"Well, can't you avoid that particular foreign relations problem by simply deporting these people?" Scalia asked. "Free them from the jails and send them back to the countries that are objecting. What's the problem with that?

"We have to enforce our laws in a manner that will please Mexico. Is that what you're saying?"

The Justice Department said Arizona's population of 2 million Latinos includes an estimated 400,000 there illegally, and 60% to 70% of deportations or "removals" involve Mexican nationals.

The court hearing over the illegal immigration law comes at an interesting time. The Pew Hispanic Center this week released a report that found that Mexican immigration to the United States has come to a standstill.

The economic downturn in the United States and better conditions in Mexico, along with deportations and other enforcement, has led many to return to Mexico.

However, the debate continues as more than 10 million unauthorized immigrants -- from Mexico and other countries -- continue to live in the United States.

Even if immigration has slowed to lows not seen in decades, proponents of tough immigration laws want to beef up enforcement ahead of any future pressures.

After the arguments, Arizona Gov. Jan Brewer expressed hope the state would prevail at the high court.

"We likely will not know the court's decision for weeks," she said. "But I am filled with optimism-- the kind that comes with knowing that Arizona's cause is just and its course is true."

The administration, backed by a variety of immigrant and civil rights groups, says allowing such discretionary state authority would hurt relations between the United States and other countries, disrupt existing cooperative efforts and unfairly target legal immigrants.