"Our message today is: 'Mr. President, we listened, and we came out in record massive numbers to support you,'" Gutierrez said. "We need you to support us today."
Obama has called the new law "misguided" and instructed the Justice Department to examine it to see if it's legal. It requires police to question people about their immigration status -- including asking for identification -- if they suspect someone is in the country illegally. Opponents say it would lead to racial profiling because officers would be more likely to ask people who look Hispanic.
Supporters have dismissed concerns about profiling, saying the law prohibits the use of race or nationality as the sole basis for an immigration check. Gov. Jan Brewer, who signed the measure Friday, has ordered state officials to develop a training course for officers to learn what constitutes reasonable suspicion someone is in the United States illegally.
U.S. Rep. Raul Grijalva, an Arizona Democrat, promised to march in the streets and invite arrest by refusing to comply.
"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.
Protesters, some of whom came from as far away as Texas, clustered under trees for shelter from the searing sun and temperatures that approached 90 degrees. Police said it was peaceful and there were no clashes.
Bill Baker, 60, took time off work at a downtown restaurant to sell umbrellas and Mexican and American flags to the largely Hispanic crowd. He said he wasn't making much money, but he wanted to help them exercise their freedom of expression -- even though he supports the law they all showed up to oppose.
"If I go to another foreign country, if I go to Mexico, I have to have papers," Baker said. "So I don't feel there's anything particularly harsh about the law."
He said he's worried the bill will hurt the economy if many of Arizona's estimated 460,000 illegal immigrants leave the state and stop spending money here.
"But that's the price you have to pay to have a lawful country," Baker said.