PHOENIX – The furor over Arizona’s new law cracking down on illegal immigrants grew Monday as opponents used refried beans to smear swastikas on the state Capitol, civil rights leaders demanded a boycott of the state, and the Obama administration weighed a possible legal challenge.

Activists are planning a challenge of their own, hoping to block the law from taking effect by arguing that it encroaches on the federal government’s authority to regulate immigration and violates people’s constitutional rights by giving police too much power.

The measure — set to take effect in late July or early August — would make it a crime under state law to be in the U.S. illegally. It directs police to question people about their immigration status if there is reason to suspect they are illegal.

“If you look or sound foreign, you are going to be subjected to never-ending requests for police to confirm your identity and to confirm your citizenship,” said Alessandra Soler Meetze, executive director of the American Civil Liberties Union of Arizona, which is exploring legal action.

Employees at the Capitol came to work Monday to find that vandals had smeared swastikas on the windows. And protesters gathered for a second day to speak against a law they say will lead to rampant racial profiling of anyone who looks Hispanic.

The White House would not rule out the possibility that the administration would take legal action against Arizona. President Barack Obama, who warned last week that the measure could lead to police abuses, asked the Justice Department review the law’s implications before deciding how to proceed.

Mexican President Felipe Calderon said the law is discriminatory and warned that trade with Arizona will be strained.

Currently, many U.S. police departments do not ask about people’s immigration status unless they have run afoul of the law in some other way.

Under the new Arizona law, immigrants who can’t show they are allowed to be in the U.S. could be arrested, jailed for up to six months and fined $2,500. That is a significant escalation of the typical federal punishment for being here illegally — deportation.

People arrested by Arizona police would be turned over to federal immigration officers. Opponents said the federal government could thwart the law by refusing to accept them.

Supporters of the law said it is necessary to protect Arizonans from crimes committed by illegal immigrants. Arizona is home to an estimated 460,000 illegal immigrants.

Republican Gov. Jan Brewer, who signed the bill on Friday, said Arizona must act because Washington has failed to stop the flow of illegal immigrants and drugs from Mexico. Brewer has ordered state officials to develop training for officers to learn what constitutes reasonable suspicion that someone is in the U.S. illegally.

The crux of opponents’ arguments is that only the federal government has the authority to regulate immigration.

“If every state had its own laws, we wouldn’t be one country; we’d be 50 different countries,” said Thomas Saenz, president and general counsel of the Mexican American Legal Defense and Educational Fund.