(CNN) -- These days, Jessica Mejia doesn't leave the house without three pieces of identification to prove her citizenship.

Mejia, a University of Arizona student who was born and raised in Tucson, says the habit formed last week, after a series of raids in Arizona targeting illegal immigrants. And now, a new state law that cracks down on illegal immigration has given her more cause for concern.

"Even if you're legal, you're in fear that maybe your driver's license isn't going to be enough or if you're walking down the street and the police stop you," said Mejia, 21. "It's a constant fear we're living in and even legal citizens are afraid to go out."

Senate Bill 1070 is set to take effect in August or September, if it withstands legal challenges that a number of groups who oppose the legislation are expected to raise.

Mejia's concerns were echoed by others in Tucson and across the country who oppose the legislation, which requires police to question people if they have reason to suspect they're in the United States illegally.

Mejia, who helped organize a protest in front of the state capitol Friday, is one of many student activists in Arizona organizing against SB 1070.

Protests continued Sunday outside the capitol building in Phoenix, with hundreds gathering in a largely peaceful demonstration against the new measure.

Read about Sunday's protest

The law also requires legal immigrants to carry their alien registration documents at all times. But U.S. citizens like Mejia, who identifies herself as Chicana, says she carries her driver's license, voter registration card and school fingerprint card at all times out of fear of being racially profiled.

"How can you tell what will give an officer reasonable suspicion to stop you?" she said. "We understand there's a need for protection on the border, but we think it should come more with immigration reform, not by pulling over people and stopping them on the street."

Opposition to the bill is also coming from elected officials at various levels of government in Arizona. Phoenix Mayor Phil Gordon said he has scheduled an item for the Tuesday session of City Council to prepare for legal action against SB 1070.

"I will direct the city manager and city attorney to file a lawsuit against the state to enjoin the law from going into effect and have it declared unconstitutional," he said.

Supporters of the law say it fills a void left by the federal government's failure to properly address immigration reform.

"One of the few enumerated, delegated and specified duties and powers given to the federal government in the Constitution is to provide for the common defense of the nation. In this they have failed by not securing the border and by not keeping immigration law up to date with the needs of our nation," said CNN iReporter Tom B., a defense contractor in Iraq who didn't want his last name to be used for security reasons.

Read why iReporter supports law

"This law will allow local law enforcement in the course of their duties to question individuals in regards to their immigration status. Since Arizona is a border state they are the site of the main issue at hand," he said in an e-mail.

Arizona state Rep. Russ Jones, who voted for the bill, said the state felt compelled to craft its own legislation.

"Until the federal government actually puts up an effective border fence securing our southern border, we cannot sit back and hope for the best while our laws are broken every day and the hands of law enforcement are tied."

Read more from Rep. Russ Jones

Gov. Jan Brewer signed the legislation Friday, citing border-related crime as a key factor. She also issued an executive order that requires additional training for local officers on how to implement the law without engaging in racial profiling or discrimination.

The rules, to be established in by the Arizona Peace Officers Standards and Training Board, are due back to her in May. The law goes into effect 90 days after the close of the legislative session, which has not been determined.

Other police organizations that support the bill, including the Phoenix Law Enforcement Association, say the legislation has numerous safeguards to protect the rights of minority groups.

"The bill requires reasonable suspicion for officers to make contact and also contains language that allows officers discretion in enforcing the law," a statement on the group's website says. "Officers cannot stop a person based solely on race, color, or national origin."

The Arizona Association of Chiefs of Police, which had opposed the measure, issued a statement saying, "Law enforcement professionals in the state of Arizona will enforce the provisions of the new law to the best of their abilities."

The bill's passage immediately triggered vows from advocacy groups across the country to pursue legal action to stop it in its tracks.

Victor Viramontes, senior legal counsel for the Mexican American Legal Defense and Education Fund, said his organization plans to ask the federal government for a permanent injunction to prevent the law from taking effect.

"What we need is singular immigration policy, and that's what the Constitution mandates. The Arizona statute stands in the way of the federal government's ability to do its job by overwhelming the system," Viramontes said.

Most undocumented immigrants follow the laws of the country, Viramontes said, and deserve the same human rights afforded U.S. citizens.

"Sometimes it's politically expedient to target undocumented immigrants and push them further into shadows, but they're already some of the most vulnerable to civil rights abuse, and the Legislature's role should be to protect these contributing members of society."

On the ground in Arizona, students and young people are at the forefront of the fight, using social media and technology to organize.

"As soon as [Brewer] signed that bill it shook the hornet's nest. It awoke not only Arizona, not only our community, but the nation," said Jeff Santino, a student organizer and graduate student at the University of Arizona. "People are all flooding us with support and I think we need to garner that support."

Mejia said her generation owes it to future generations to ensure they don't grow up in a society that legalizes discrimination. She said she also feels a debt to her parents and grandparents, who may be too busy working to support their families to engage in a political fight.

"I feel like it's a really big responsibility on our shoulders to protect our community when they don't have voice in what's going on."

CNN's Thelma Gutierrez contributed to this report.