"We have some deep concerns with the law from a law enforcement perspective because we believe it will detract from and siphon resources that we need to focus on those in the country illegally who are ... committing the most serious crimes in addition to violating our nation's immigration laws," she said.
Attorney General Eric Holder said that he feared the new law would be "subject to potential abuse."
In Federal Plaza in Manhattan, the bill was seen as anti-American.
"Immigrants across this country are coming here for a better life and to contribute to this nation socially and economically, and this law doesn't move in the direction that we should be, of recognizing immigrants for what their contributions," Liu said.
Disagreement over the legislation has even split political families. Arizona Sen. John McCain has taken a hard-line stance in favor of his state's new law, but his daughter Meghan blogged her disagreement.
"I believe it gives the state police a license to discriminate," wrote Meghan McCain.
Hasan Mohammed, who immigrated to New York from Ghana three years ago, said that the law does not make sense to him.
"Why should they sign a bill to deport immigrants? America is a state of immigrants," he said. "It's inhumane."
Joshua Epstein, an attorney for the Immigrant Defense Project, told ABCNews.com that as a member of an immigrant family he feels personally targeted by the bill.
"It tears me apart, it tears me apart that my country would purposely destroy families and people that are here to live and contribute to our great country of immigrants," said Epstein.
The state may pay for the legislation with a loss of business.
Elizabeth Barna, a lawyer with the American Immigration Lawyers Association, said that the organization voted nearly unanimously to cancel a convention scheduled to be held this fall in Arizona.
"The law is terrible. It's going to foster racism and there will be racial profiling, there is no doubt," Barna said.
The San Francisco Board of Supervisors will also consider today a resolution that would result in the city ending contracts with Arizona-based businesses, according to the San Francisco Chronicle.
"We want to send a message," Supervisor David Campos said at a rally today. "There are consequences when you target a whole people."
Even a lawmaker from Arizona is urging a boycott of the state. Democratic Rep. Raul Grijalva from Tucson released a statement late last week urging conventions not to come to Arizona until the state overturns the immigration bill.
"Just as professional athletes refused to recognize Arizona until it recognized Martin Luther King Jr., we are calling on businesses and organizations not to bring their conventions to Arizona until it recognizes civil rights and the meaning of due process," Grijalva said.
Los Angeles' Spanish daily newspaper La Opinión called for a national boycott of Arizona in an editorial, writing, "We call on those who believe in the U.S. Constitution to boycott the state of Arizona."
"The anti-immigrant bill signed yesterday in Arizona is a violation of our right to be free from police harassment based on the way we look," the paper stated.
All these boycot calls have some Arizona business owners worried. For the first time since he opened Portland's Restaurant in Phoenix nine years ago, owner Dylan Bethge is concerned about his business.