NEW YORK (CNNMoney.com) - With the debate over immigration heating up in Washington and across the country, hundreds of thousands of people skipped work and avoided trips to stores and restaurants Monday to demonstrate the economic power of immigrants.

Javier, a Mexican dishwasher working in New York City, joined the protest in Union Square, "we are not criminals, we didn't come here to steal from anyone. We're just doing work that others won't do." Javier, who said he works 12 hour shifts, admitted "I'm afraid, because my boss didn't really want me to come here, but I came because I wanted to claim my rights as a worker."

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Javier, who held up a Mexican flag and an American flag, marched with his wife and child and several of his coworkers, but he said the rest of his coworkers "were afraid to come because they were afraid they would lose their jobs."

The boycott is designed to pressure Congress to grant amnesty to the estimated 11 to 12 million unauthorized immigrants living in the United States.

But even some people supporting immigrant workers said the day might not live up to its original billing.

"The day itself has been tempered from the original way it was supposed to play out," according to Dawn Lurie, an immigration lawyer based in Washington, noting that many people in the end decided against protesting.

"If everyone were to participate I think there would be areas of the country that would just be frozen and there would be an incredible economic impact, but we're just not going to see that,” she said.

Several big companies, including Tyson Foods and Cargill, the nation’s largest meat processors, suspended operations at some plants in the Midwest and other regions due to an expected lack of workers. (Full story.)

In California, upscale Los Angeles restaurant Jar was one of the many eating establishments in the area that decided to close for the day.

"We don't want to be responsible for anything that might happen to our guests or the restaurant," said Dan Harrington, operations manager at Jar, referring to the possibility of violence or unrest.

"It wasn't political. It was a better business decision," Harrington said, although he noted that there hadn't been any trouble in the area around the restaurant.

Other small- and mid-sized businesses closed their doors, either in support of the protests or because they believe it would be difficult to do business.

Even some of those employers doing business as usual have put contingency plans in place.

Some hired additional staff in case employees didn't show up or staggered shifts so workers could attend the rallies for part of the day. A few offered time and a half to encourage their employees to come to work.

Angelo Amador, director of immigration policy at the U.S. Chamber of Commerce, which represents the nation's big businesses, said before Monday's rally: "I don't think there's going to be a great economic impact.

"However," he added, “the moment one plant closes you have an economic impact."

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Note: How could the immigrant walkout affect you? Watch Lou Dobbs Tonight, 6 p.m. ET on CNN.

What immigration reform could cost you. More here.

For more on the May 1 immigration rally, click here.