A court suit from 15-year Tucson police veteran Martin Escobar was one of three filed Thursday, less than a week after Republican Gov. Jan Brewer signed the bill that critics claim is unconstitutional and fear will lead to racial profiling.
U.S. Attorney General Eric Holder has said the federal, which requires local and state law enforcement to question people about their immigration status if there's reason to suspect they're in the country illegally, and which makes it a state crime to be in the United States illegally.
Brewer and other backers say the state law is necessary amid the federal government's failure to secure the border and growing anxiety over crime related to illegal immigration.
CBS News correspondent Bill Whitaker reports 70 percent of Arizona residents say they're in favor of the law, according to a new poll.
"Mexican-Americans are not going to take this lying down," singer Linda Ronstadt, a Tucson native, said at a news conference on a lawsuit planned by the American Civil Liberties Union, the Mexican American Legal Defense and Educational Fund and the National Immigration Law Center.
Colombian singerto meet the city's police chief and mayor amid her concerns the measure would violate human and civil rights.
"It goes against all human dignity." she said.
At the Billboard Latin Music Awards ceremony in Puerto Rico, singer Ricky Martin denounced the law, too, saying it "makes no sense."
Arizona is already getting hit in the pocketbook, reports Whitaker. Cities across the country are threatening to boycott the state and eight conventions have decided to pull out of Phoenix - each could cost the city up to $45,000.
While divisive debate over the law swirled nationwide, Arizona lawmakers Thursday approved modifications to the law that requires local and state law enforcement to question people about their immigration status if there's reason to suspect they're in the country illegally, and makes it a state crime to be in the United States illegally.
The changes include strengthening restrictions against using race or ethnicity as the basis for questioning by police and specifying that possible violations of local civil ordinances can trigger questioning on immigration status.
The law's sponsor, Republican Sen. Russell Pearce, characterized those changes as clarifications "just to take away the silly arguments and the games, the dishonesty that's been played."
Some Latin nations also entered the debate.
In Mexico City, Mayor Marcelo Ebrard announced he would try to join lawsuits seeking to overturn the law, with a statement from his office calling the measure "a planned Apartheid against Mexicans."
And officials in El Salvador urged countrymen to avoid traveling to Arizona, according to the Foreign Ministry. In Nicaragua, officials called on the Organization of American States and the United Nations "to take the necessary measures to safeguard the rights of the Hispanic population."
The National Coalition of Latino Clergy and Christian Leaders, and sought an injunction preventing authorities from enforcing the law. The group argued that federal law pre-empts state regulation of national borders, and that Arizona's law violates due process rights by letting police detain suspected illegal immigrants before they're convicted.
In filing his suit, Escobar, argued that there's no way for officers to confirm a person's immigration status without impeding investigations, and that the new law violates constitutional rights. Tucson police said Escobar acted on his own.
Separately, a Phoenix police officer filed a lawsuit arguing he'll be sued whether he enforces the law or not, either for violating civil rights or for refusing to enforce it.
At least three Arizona cities - Phoenix, Flagstaff and Tucson - are considering legal action to block the law.
About 40 immigrant rights activists gathered outside Wrigley Field in Chicago Thursday as the Cubs open a four-game series against the Diamondbacks. A small plane toting a banner criticizing the law circled the stadium. A Cubs spokesman declined to comment, while Arizona manager A.J. Hinch said the team was there to play baseball.
Politicians from around the country also weighed in. Colorado Gov. Bill Ritter said he would veto a new law like the one in Arizona, while Texas Republican Gov. Rick Perry said such a law would be wrong for his state because it has a tradition of rejecting harsh anti-immigrant policies.
Supporters of the new law also were vocal outside Arizona.
A group of conservative state lawmakers in Oklahoma said they plan to introduce a bill similar to Arizona's. In Texas, Rep. Debbie Riddle, a Republican, said she will introduce a measure similar to the Arizona law in the January legislative session. And Republicans running for governor in Colorado and Minnesota expressed support for the crackdown.