For a second straight day, hundreds of youths marched, chanted and carried signs throughout San Diego County streets Tuesday to protest an immigration bill under consideration by the U.S. Senate.Tuesday morning, some 800 students from San Diego city schools walked out of classes to protest the proposed law, said Jim Esterbrooks of the county Office of Education.School police officers followed along with the teens as they demonstrated noisily but peaceably, said Music McCall of the San Diego Unified School District.As it did Monday, San Diego's march ended with a large and boisterous rally at Chicano Park in Barrio Logan. The participants remained largely well- behaved, and there were no arrests, SDPD spokesman Dave Cohen said.The Sheriff's Department sent patrol personnel to monitor similar rallies in Lemon Grove, Santee, Fallbrook, San Marcos and Vista.In the latter city, deputies arrested one unruly demonstrator around noon, said a department spokeswoman.In Escondido, officers escorted about 600 middle- and high-schoolers who skipped classes and marched without incident across the city and to Cal State San Marcos for a late-morning protest rally, said EPD Lt. Tom Albergo.That outcome was a definite improvement over the demonstration that took place in Escondido on Monday, when protesters hurled rocks and bottles at police and two dozen people -- mostly minors -- were arrested.Tuesday morning, about 200 students from Madison High School and Bell Junior High peacefully marched toward Clairemont High School in San Diego to rally more students.Those participating in the walkouts were "considered to be in defiance of district rules" and will be subject to discipline, possibly including detention or suspension, McCall said.Tuesday morning, about 500 students from Vista and Rancho Buena Vista high schools marched on Main Street toward City Hall. Many protestors hoisted Mexican flags in the air."We're not criminals," chanted a crowd of Vista students who claimed their parents were illegal immigrants. "We pay our taxes.""If not for the Mexicans, you all would be nothing here," one student said.The protests, which have flared throughout Southern California, target a bill passed by the House of Representatives in December that would require employers to verify Social Security numbers with the Department of Homeland Security, increase penalities for immigrant smuggling and stiffen penalities for undocumented immigrants who reenter the United States after having been removed.Under the legislation, local law enforcement agencies would be reimbursed for detaining illegal immigrants.Illegal immigrants with aggravated felony convictions would also be barred from receiving green cards.The U.S. Senate's Judiciary Committee softened the bill Monday by voting to create a path for some of the nation's estimated 12 million illegal immigrants to become citizens without first leaving the country.Under the version voted on by the committee, additional foreign workers would be allowed to enter the United States temporarily under a program that also could lead to citizenship.Additionally, the committee adopted an amendment by Sen Richard Durbin, D- Ill., that would protect charitable organizations and churches from criminal charges for providing aid to illegal immigrants.The bill will now move to the Senate floor, where an intense debate likely to pit Republicans against each other is expected to begin this week.