More were planned Monday after thousands gathered this weekend to demonstrate against that will make it a state crime to be an illegal immigrant in Arizona.
Opponents say the law will lead to rampant and turn Arizona into a police state with provisions that require police to question people about their immigrant status if they suspect they are here illegally. Day laborers can be arrested for soliciting work if they are in the U.S. illegally, and police departments can be sued if they don't carry out the law.
But Phoenix Mayor Phil Gordon says many supporters of the law are not just misguided but also racist, reports CBS News correspondent John Blackstone.
"It's just morally wrong," he told Blackstone. "This country is not about having people wear arm bands with Jewish stars or in this case Hispanic brown symbols," Gordon said. He also called the law "clearly unconstitutional."
But supporters of the law, set to take effect in late July or August, say it is necessary to protect Arizonans from a litany of crimes committed by illegal immigrants. Arizona is home to an estimated 460,000 illegal immigrants.
The controversial Maricopa County Sheriff Joe Arpaio says his department has arrested some 38,000 illegal immigrants in the past three years and the new law will give him the tools to step up his efforts to combat the flood coming across Arizona's border with Mexico.
"I will arrest the people that are here under that new misdemeanor law and book them into our jails," Arpaio said.
Gov. Jan Brewer, who signed the bill on Friday, argues Arizona must act because the federal government has failed to stop the steady stream of illegal immigrants and drugs that move through Arizona from Mexico.
The fallout over the dispute spread across the border Monday as Mexican President Felipe Calderon said the law is discriminatory and warned relations with the U.S. border state will suffer. Calderon says trade and political ties with Arizona will be "seriously affected," although he announced no concrete measures.
The law has revved up the national debate, drawing the attention of the Obama administration and Congress. Obama has called the new law "misguided" and instructed the Justice Department to examine it to see if it's legal.
The new law makes it a crime under state law to be in the country illegally. Immigrants unable to produce documents showing they are allowed to be in the U.S. could be arrested, jailed for up to six months and fined $2,500.
Arizona officers would arrest people found to be undocumented and turn them over to federal immigration officers. Opponents said the federal government can block the law by refusing to accept them.
Democratic Rep. Raul Grijalva asked the federal government not to cooperate when illegal immigrants are picked up by local police.
State Sen. Russell Pearce, the Republican who sponsored the legislation, said it's "pretty disappointing" that opponents would call on the federal government to refuse to cooperate with Arizona authorities.
"It's outrageous that these people continue to support law breakers over law keepers," Pearce said Sunday.
Grijalva and civil rights activists promised to march in the streets and invite arrest by refusing to comply with the law. Police said the protests Sunday were peaceful and there were no clashes.
"We're going to overturn this unjust and racist law, and then we're going to overturn the power structure that created this unjust, racist law," Grijalva said.
U.S. Rep. Luis Gutierrez, D-Ill., called on Obama to live up to a campaign promise to pass immigration reform. Gutierrez is one of the nation's loudest voices calling for comprehensive immigration reform that would create a pathway to citizenship for the millions of illegal immigrants now in the United States.
"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. Brewer has ordered state officials to develop a training course for officers to learn what constitutes reasonable suspicion that someone is in the U.S. 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.