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“Our message today is: ‘Mr. President we listened, and we came out in record massive numbers to support you,’” he said. “We need you to support us today.”

The law has drawn support from many in Arizona who are fed up with the many problems brought on by illegal immigration.

“If I go to another foreign country, if I go to Mexico, I have to have papers,” said Bill Baker, 60, who took time off work at a downtown Phoenix restaurant to sell umbrellas and Mexican and American flags to the largely Hispanic crowd of protesters. “So I don’t feel there’s anything particularly harsh about the law.”

Supporters have dismissed concerns about profiling, saying the law prohibits the use of race or nationality as the sole basis for an immigration check. Mrs. Brewer has ordered state officials to develop a training course for officers to learn what constitutes reasonable suspicion that someone is in the United States illegally.

Current law in Arizona and most states doesn’t require police to ask about the immigration status of those they encounter, and many police departments prohibit officers from inquiring out of fear immigrants won’t cooperate in other investigations.

The March 27 shooting death of rancher Rob Krentz on his property in southeastern Arizona brought illegal immigration and border security into greater focus in the state. Authorities believe Krentz was killed by an illegal border crosser.