Brewer met privately with tourism industry leaders and later told reporters that she was forming a group of industry representatives and state officials to prepare a marketing strategy to deal with public criticism of the law.
The law, which is set to take effect late July, requires police to ask a person about his or her immigration status if there's "reasonable suspicion" that the person is in the country illegally. Being in the country illegally would be a state crime under the law.
Critics have said the law could lead to racial profiling, and some groups and city governments have called for. Arizona's tourism board estimates it is losing $90 million to boycotts already, reports CBS News correspondent Bill Whitaker.
Brewer said those charges that the law will produce racial profiling are unfounded, and she said the law specifically prohibits racial profiling.
She also said people mistakenly believe that just anybody walking on a street could be asked to produce identification.
"The bottom line is there are a lot of mistruths about the bill," she said. "You're not going to walk down the street and get questioned unless you've committed a crime."
Tourism industry representatives didn't request changes in the law, said Brewer and Debbie Johnson, head of a statewide hotel association and of a statewide tourism industry coalition.
"There was no discussion of it," Johnson said.
The state will provide startup funding of $250,000 for the marketing campaign, which will start by reviving a past effort to urge Arizonans to vacation in their own state, Johnson added.
Other details, including what messages to aim to non-Arizonans, haven't been decided, Johnson said.
Brewer said she was concerned about the boycott calls, saying lost trade would harm the state, its tourism industry and "a lot of innocent people."
"We want everyone to continue to come here," she said.
Johnson, president of the Arizona and Lodging Association and president of the Arizona Tourism Alliance, said boycotts intended to pressure the state's policymakers are misguided because they mainly hurt people working in the state's tourism-related businesses.
"The concern is about the 200,000 families that are trying to make a living," she said.
Brewer said the "truth-telling" task force would try to develop ways to "rebrand or reposition Arizona's brand."
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