WASHINGTON (AP) - Supreme Court justices strongly suggested Wednesday that they are ready to allow Arizona to enforce part of a controversial state law requiring police officers to check the immigration status of people they think are in the country illegally.

Liberal and conservative justices reacted skeptically to the Obama administration's argument that the state exceeded its authority when it made the records check, and another provision allowing suspected illegal immigrants to be arrested without a warrant, part of the Arizona law aimed at driving illegal immigrants elsewhere.

"You can see it's not selling very well," Justice Sonia Sotomayor told Obama administration Solicitor General Donald Verrilli.

It was unclear what the court would do with other aspects of the law that have been put on hold by lower federal courts. The other blocked provisions make it a state crime for immigrants not to have immigration registration papers and for illegal immigrants to seek work or hold a job.

Gov. Jan Brewer, who signed the law two years ago, was on hand for the final argument of the court's term.

The latest high court clash between the administration and states turns on the extent of states' role in immigration policy, which is essentially under the federal government's control.

Verrilli tried to persuade the justices that they should view the law in its entirety and inconsistent with federal immigration policy. He said the records check would allow the state to "engage effectively in mass incarceration" of undocumented immigrants.

But Chief Justice John Roberts was among those on the court who took issue with Verrilli's characterization of the check of immigration status, saying the state merely wants to notify federal authorities it has someone in custody who may be in the U.S. illegally. "It seems to me that the federal government just doesn't want to know who's here illegally and who's not," Roberts said.

Outside the courthouse, more than 200 protesters gathered. The law's opponents made up a clear majority of the crowd, chanting and carrying signs like "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.

The administration challenged the law in federal court. Alabama, Georgia, Indiana, South Carolina and Utah passed similar laws, parts of which also are on hold pending the high court's decision.

The court argument took place as presumptive Republican nominee Mitt Romney is trying to find a way to cut President Barack Obama's strong support among Latino voters. Romney was drawn to the right on issues like immigration as he fought off other Republicans in state GOP primary elections. On Monday, Romney signaled he was considering a wide range of immigration policies, including a proposal from Sen. Marco Rubio, R-Fla., that would allow some of the estimated 11 million illegal immigrants a chance at visas to stay in the U.S.

A decision in the high-profile immigration case is expected in late June as both camps will be gearing up for the general election.

Arizona argues that with its 370-mile border with Mexico, it has paid a disproportionate price for illegal immigration. It says its 2010 law is consistent with federal immigration policy.

The administration says the law, and Arizona's approach of maximum enforcement, conflict with a more nuanced federal immigration policy that seeks to balance national security, law enforcement, foreign policy, human rights and the rights of law-abiding citizens and immigrants.

Civil rights groups that back the administration say Arizona's and the other states' measures encourage racial profiling and ethnic stereotyping. 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.