Demonstrators demanded an overhaul of immigration laws Wednesday in an annual, nationwide ritual that carried a special sense of urgency as Congress considers sweeping legislation that would bring many of the estimated 11 million people living in the U.S. illegally out of the shadows.

Thousands joined May Day rallies from Concord, N.H., to Los Angeles, where scores of marchers gathered downtown. In Salem, Ore., Gov. John Kitzhaber was cheered by about 2,000 people on the Capitol steps as he signed a bill to allow people living in Oregon without proof of legal status to obtain drivers licenses.

In Vermont, more than 1,000 people assembled on the Montpelier Statehouse lawn. And in New York, paper rats on sticks bobbed along Sixth Avenue as about 200 protesters set off from Bryant Park, chanting: “What do we want? Justice! When do we want it? Now!” The rats were intended to symbolize abused migrant workers.

The May Day crowds paled in comparison to the massive demonstrations of 2006 and 2007, during the last serious attempt to introduce major changes to the U.S. immigration system. Despite the large turnouts six years ago, many advocates of looser immigration laws felt they were outmaneuvered by opponents who flooded congressional offices with phone calls and faxes at the behest of conservative talk-radio hosts.

Now, immigrant advocacy groups are focusing heavily on calling and writing members of Congress, using social media and other technology to target specific lawmakers. Reform Immigration for America, a network of groups, claims more than 1.2 million subscribers, including recipients of text messages and Facebook followers.

Many of Wednesday’s rallies featured speakers with a personal stake in the debate. Naykary Silva, a 26-year-old Mexican woman in the country illegally, joined about 200 people who marched in Denver’s spring snow, hoping for legislation that would ensure medical care for her 3-year-old autistic son.

“If you want to do something, you do it no matter what,” Silva said. “There’s still more work to do.”

Police in New York restrained several demonstrators, but the marches were peaceful. In downtown Seattle, dozens gathered under heavy police presence, one year after some protesters broke windows and set fires.

The New York crowd was a varied bunch of labor groups, immigrant activists and demonstrators unaffiliated with any specific cause. Among them was 26-year-old Becky Wartell, who was carrying a tall puppet of the Statue of Liberty.

“Every May Day, more groups that have historically considered themselves separate from one another come together,” she said.

Gabriel Villalobos, a Spanish-language talk radio host in Phoenix, said many of his callers believe it is the wrong time for marches, fearful that that any unrest could sour public opinion on immigration reform. Those callers advocate instead for a low-key approach of calling members of Congress.

“The mood is much calmer,” said Villalobos, who thinks the marches are still an important show of political force.

May Day rallies began in the United States in 2000 during a labor dispute with a restaurant in Los Angeles that drew several hundred demonstrators, said Angelica Salas, executive director of the Coalition for Humane Immigrant Rights of Los Angeles. Crowds grew each year until the House of Representatives passed a tough bill against illegal immigration, sparking a wave of enormous, angry protests from coast to coast in 2006.

The rallies, which coincide with Labor Day in many countries outside the U.S., often have big showings from labor leaders and elected officials.