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(CBS) LOS ANGELES Violence broke out between immigration rights advocates and police officers Tuesday after a day of peaceful marching through downtown Los Angeles.

About 10,000 people waving American and Mexican flags marched from City Hall to MacArthur Park, including 1,480 Los Angeles Unified School District students. Organizers had predicted lower turnout, blaming stepped-up immigration raids, frustration that Congress hasn't passed immigration reform, and an effort by many groups to shift their focus from street mobilizations to citizenship and voter registration drives.

The violence stemmed from the throwing of a bottle at police officers, dressed in riot gear, who acted quickly to quell the disturbance.

Though fewer in number, protesters did show up in cities from Miami to Chicago to Los Angeles. But amid the waving flags, hand-painted signs and chants, many protesters' frustration was palpable.

"After working 22 years here, paying taxes and being a good citizen, I think it's fair they give me residency," said Los Angeles protester Manuel Hernandez, 38-year-old Mexican who along with his wife and two children is undocumented. "It's not fair we don't have documents."

In Los Angeles, where May 1 protests in 2006 brought out several hundred thousand at various activities, about 25,000 came out for a downtown rally, said police Capt. Andrew Smith. A second rally was expected Tuesday evening.

After massive marches in the spring of 2006, the Senate passed a sweeping bill that would have provided a path to citizenship for many of the nation's 12 million illegal immigrants.

But the bill was never reconciled with the then-Republican-controlled House, and legislation has languished since last summer. Subsequent bipartisan proposals, which have not been formally taken up by Congress, have gotten more conservative.

Meanwhile, federal immigration raids and deportations are increasing.

In fiscal year 2006, federal immigration officials deported 195,024 people, compared with 173,363 the previous year, according to U.S. Immigration and Customs Enforcement data. Six months into the current fiscal year, 125,405 have been deported.

Protesters said that while anger over raids brought some people out, fear also kept many at home.

Schoolteacher David Cid said his students were suffering because raids had separated families. Los Angeles County has about 1 million illegal immigrants, the largest concentration in America.

"They feel terrorized," said Cid, who declined to give more details about where he works to protect his students.

Democratic Party chairman Howard Dean told immigrant supporters in Miami that a reform bill before Congress was "insane" because it would require many illegal immigrants to return home before applying for citizenship.

"This is a government that can't find a 6-foot-4 terrorist. How is it going to find 12 million people?" he told a group of more than 100 party supporters at Miami's Parrot Jungle Island.

Some groups had called for an economic boycott and hoped for a repeat of last year, when thousands of immigrants and students stayed away from work and school in a sign of solidarity.

Other groups rejected the boycott, arguing it puts immigrants' livelihoods at risk and deprives children of valuable classroom time.

For Eliseo Medina -- executive vice president of the Service Employees International Union, a major organizer of rallies last year that has shifted to citizenship and voter registration drives -- it's clear what's needed.

"For the future, we'll need to have a more organized movement, and we are on the way to building that," she said.