PHOENIX — In the place where it all began, there was confusion and consternation on Monday at the United States Supreme Court’s unanimous decision to uphold the most controversial portion of Arizona’s contentious immigration law, the part that requires law enforcement officers to check the immigration status of people in custody who they suspect are in the country illegally.

Many legislators, activists and Latinos here had expected that part of the ruling to go exactly the way it did. What they did not expect was for the court, at the same time, to place so many limits on police powers.
Under the ruling, the police cannot hold illegal immigrants in local jails merely because of their status or prohibit them from seeking employment in Arizona, drawing clear lines between state and federal jurisdiction over immigration enforcement.
So there was also surprise and a measured sense of victory from all sides over the mixed decision, as well as questions about what could happen next.
During a news conference at the State Capitol here, Gov. Jan Brewer, a Republican who fervently championed the law, chose to overlook the rulings against the law, saying “the heart” of the law, known as SB 1070, “has proven to be constitutional” and the state’s authority to “protect its people” from the dangers of illegal immigration had been upheld.
“Arizona did not ask for this,” Governor Brewer said, “but we’re here today because the federal government has failed the American people” by failing to secure the Mexican border.
On a patch of grass just outside the Capitol, Senator Steve M. Gallardo, a Democrat, said the Supreme Court had sent the governor “a loud message,” telling her she had gone too far in trying to expand her reach into “an issue that is clearly a federal issue.”
Lost in the middle were people like Honorio Hernández, 35, and Jorge Martínez, 49. They are Mexican immigrants living here under different circumstances — Mr. Hernández is a legal resident, Mr. Martínez is not — but both are nonetheless troubled by the prospect of facing the police.
“Will they be able to stop me because I look the way I look?” Mr. Hernández asked as he stepped outside Ranch Market on North 16th Street, a mecca for Hispanic goods.
“Before, I could get stopped and get a ticket for driving without a license,” said Mr. Martínez, nearby. “Now, they’re going to ask for my papers. Then, what?”
In affirming federal jurisdiction over immigration, the Supreme Court ruled that it is up to federal — not state — authorities to arrest immigrants if being here illegally is their only offense. So on Monday at the office of Puente, an advocacy group here, workers spent hours urging supporters to join a protest outside the federal immigration offices later in the day. It was a marked shift for an organization whose main target had been Sheriff Joe Arpaio of Maricopa County, who has waged a relentless crackdown against Latinos. In the wake of Monday’s ruling, officers with the Department of Homeland Security in Arizona are being reminded to focus on serious criminals and repeat offenders when pursuing deportation, part of a push by the Obama administration to ease the impact of tough enforcement in immigrant communities.
The administration also revoked on Monday an agreement allowing certain Arizona law enforcement officers to enforce federal immigration laws.
Meanwhile, throughout the state, in an effort to avoid claims of racial profiling, police officers and sheriff deputies are being trained — through an updated version of a video made in 2010, when Governor Brewer signed SB 1070 into law — to understand what are considered reasonable signs that a person might be an illegal immigrant.
A lack of government-issued identification, a foreign vehicle registration or an inability to provide a residential address are among the objective causes for suspicion listed in the video. Others are more subjective, like a person’s “unexplained nervousness or inability to make eye contact,” “dress” or “significant difficulty communicating in English.”
The police chief here, Daniel García, said his department has gone beyond the training, posting messages to the community online and offering additional training to its officers “in a manner to ensure equal justice under the law is provided to every person irrespective of race, color or national origin.”
Chief García went on, “I want the citizens of Phoenix to have a voice and that includes everyone, all individuals.”
Some people here were still skeptical, though. Rosario Pérez, 46, a Mexican immigrant and legal resident who was also shopping at Ranch Market on Monday, said she carries her Social Security card wherever she goes because “Yo soy morena” — “I’m brown.”