The House of Representatives passed legislation in December that would make it a felony to be illegally in the United States, impose new penalties on employers who hire illegal immigrants and erect fences along one-third of the U.S.-Mexican border. The Senate is set to take up its own version of immigration reform on Monday.
The proposals have angered many immigrant rights groups which have promised to fight back.
The Los Angeles demonstration led to fights between black and Hispanic students at one high school, but the protests were largely peaceful, authorities said.
"It was horrible, horrible," Mason said. "It's ridiculous that a bunch of black students would jump on Latinos like that, knowing they're trying to get their freedom."
Chantal Mason, a sophomore at George Washington Preparatory High, said black students jumped Hispanic students as they left classes to protest the House bill that would make it a felony to be in the U.S. illegally.
Rep. Peter King of New York, one of the bill's sponsors, told CBS News correspondent Sandra Hughes, "The issue of illegal immigration, is not just a social issue, not just an economic issue, it's an issue of homeland security."
In Phoenix, police said 10,000 demonstrators marched to the office of Republican Sen. Jon Kyl, co-sponsor of a bill that would give illegal immigrants up to five years to leave the country. The turnout clogged a major thoroughfare.
"They're here for the American Dream," said Malissa Greer, 29, who joined a crowd estimated by police to be at least 10,000 strong. "God created all of us. He's not a God of the United States, he's a God of the world."
Kyl had no immediate comment on the rally.
The escalating controversy puts farmers such as Dewey Zapka of Weld County, Colo., right in the middle, CBS News' Jennifer Miller reports.
"Let them come here legal, quit chasing them," Zapka said. "Let them be comfortable here while they're working and doing our work that nobody else will do."
At least 500 students at Huntington Park High School near Los Angeles walked out of classes in the morning. Hundreds of the students, some carrying Mexican flags, walked down the middle of Los Angeles streets, police cruisers behind them.
The students visited two other area high schools, trying to encourage students to join their protest, but the schools were locked down to keep students from leaving, said Los Angeles district spokeswoman Monica Carazo.
In Georgia, activists said tens of thousands of workers did not show up at their jobs Friday after calls for a work stoppage to protest a bill passed by the Georgia House on Thursday.
That bill, which has yet to gain approval in the state Senate, would deny state services to adults living in the U.S. illegally and impose a 5 percent surcharge on wire transfers from illegal immigrants.
Supporters say the Georgia measure is vital to homeland security and frees up limited state services for people legally entitled to them. Opponents say it unfairly targets workers meeting the demands of some of the state's largest industries.
Teodoro Maus, an organizer of the Georgia protest, estimated as many as 80,000 Hispanics did not show up for work. About 200 converged on the steps of the Georgia Capitol, some wrapped in Mexican flags and holding signs reading: "Don't panic, we're Hispanic" and "We have a dream, too."
Jennifer Garcia worried what would the proposal would do to her family. She said her husband is an illegal Mexican immigrant.
"If they send him back to Mexico, who's going to take care of them and me?" Garcia said of herself and her four children. "This is the United States. We need to come together and be a whole."
On Thursday, thousands of people filled the streets of Milwaukee for what was billed as "A Day Without Latinos" to protest efforts in Congress to target undocumented workers. Police estimated more than 10,000 people joined the demonstrations and march to downtown Milwaukee. Organizers put the number at 30,000.