Alone among the justices, Antonin Scalia appeared ready to uphold the entire law, which he described as an effort by Arizona to police its borders.
When Verrilli said that Arizona's immigration law could raise foreign policy concerns, especially with Mexico, Scalia said, "So we have to enforce our laws in a manner that will please Mexico. Is that what you're saying?"
Outside the courthouse, more than 200 protesters gathered. The law's opponents made up a clear majority of the crowd, chanting and carrying signs such as "Do I Look Illegal To You?" Some shouted "shame" at Brewer when she emerged from the building after the argument.
Brewer told reporters she was "very, very encouraged" by the justices' questions.
Republicans have far outpaced Democrats in pushing tough anti-immigration laws, posing potential political problems in some states for GOP candidates including Mitt Romney. The Republicans' aggressive stand has alienated many Hispanic voters, one of the electorate's fastest-growing segments.
President Barack Obama won two-thirds of the Hispanic vote in 2008, and hopes to do better this fall. In the GOP primary contests, Romney took the harshest anti-illegal immigration stance among the top contenders, but he has had little to say lately on the issue. Romney has not taken on stand on legislation proposed by Sen. Marco Rubio, R-Fla., that would allow some undocumented immigrants a chance at visas to remain in the United States.
More than a decade ago, Republicans were making inroads among Hispanic voters. President George W. Bush, a former Texas governor, favored comprehensive immigration reform that could have established pathways to legal status for millions of illegal immigrants. But staunchly anti-illegal immigration forces gained influence in the GOP, and the reform plans were dropped.
Hispanic voters are especially important in a few battleground states that will help determine the Nov. 6 presidential election. They include Florida, New Mexico, Nevada and Colorado. Romney's problems with Hispanics also might tempt Obama's campaign to make a push in Arizona, usually a reliably Republican state.
A recent poll of Hispanic voters by the Pew Research Center found that 67 percent supported Obama, and 27 percent Romney.
A decision in the high-profile immigration case is expected in late June.
California, New York and nine other states with significant immigrant populations support the Obama administration.
Florida, Michigan and 14 other states, many of which also are challenging Obama's health care overhaul, argue that Arizona's law does not conflict with federal law.
Justice Elena Kagan, who was Obama's first solicitor general, is not taking part in the case, presumably because she worked on it while in the Justice Department.
The case is Arizona v. U.S., 11-182.
Jacques Billeaud in Phoenix and Charles Babington and Jesse J. Holland in Washington contributed to this report.
Details of immigration case: http://tinyurl.com/7ekg6ha
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