By Thomas Ferraro WASHINGTON (Reuters) - Pro-immigrant backers of a nationwide boycott set for Monday predict millions of immigrants will stay away from work, school and stores and rally in support of an overhaul of America's immigration laws. The walkout has caused a dispute over strategy within the ranks of immigrant-rights advocates, with some fearing that the action will trigger a backlash and questioning how many people will actually participate in the boycott. Yet proponents say the move is needed to prod President Bush and a divided Congress to end an election-year squabble and enact legislation to help the estimated 12 million people living illegally in the United States. "We are all losers if we continue to play this sinister game of condemning a segment of the population to live and work in the conditions of modern-day slaves," said Juan Jose Gutierrez, director of the Latino Movement USA. Boycott organizers want amnesty and eventual citizenship for illegal immigrants and predict many of America's major cities will grind to a halt as primarily Hispanic immigrants walk off their jobs, skip school and attend massive rallies. Teachers' unions in major cities have said children should not be punished for walking out of class. In New York, leaders of the May 1 Coalition organizing the boycott said a growing number of businesses had pledged to close and allow their workers to attend a rally in Manhattan's Union Square. Large U.S. meat processors, including Cargill Inc., Tyson Foods Inc. and Seaboard Corp. said they will close plants. "The Great May 1 Boycott, a day without immigrants," is a follow-up to demonstrations attended by hundreds of thousands of immigrants and their supporters across the nation on April 10. HOUSE BILL Those rallies protested a get-tough bill passed by the Republican-led House of Representatives that would reclassify illegal immigrants as felons, punish those who help them and build a fence along much of the U.S.-Mexican border. A bipartisan bill stalled in the U.S. Senate would bolster border security, but also provide illegal immigrants a path toward citizenship and a guest-worker program long favored by Bush. Bush opposes the boycott and so do many members of Congress, including Sen. Edward Kennedy, a Massachusetts Democrat helping lead a bipartisan drive to reform overall immigration laws. A Kennedy spokeswoman said the senator agrees with the position staked out by Cardinal Roger Mahony of Los Angeles, a champion of immigrant rights who has lobbied against a walkout. Mahony said a statement, "Go to work, go to school, and then join thousands of us at a major rally afterward." Secretary of State Condoleezza Rice, speaking on Sunday on CBS's "Face the Nation," said Bush favors "a comprehensive approach to immigration, where we recognize the economic role that these people play but yet keep a firm hold on border security, keep a firm hold on the fact that people have to be legal; it's extremely important." In Washington, the Rev. Graylan Scott Hagler of Ministers for Racial, Social and Economic Justice backs the boycott, but said, "If you can't take time off from work, if you can't leave school, at least stand up for immigrants."