HARRISBURG, Pa.—A bill to require contractors on taxpayer-financed construction projects in Pennsylvania to verify their employees' Social Security numbers was endorsed by a House committee Wednesday, even as dozens of people rallied against that and other Republican legislation targeting illegal immigrants.

The scope of the bill, which originally applied to public and private construction projects, was narrowed to state and local public projects by an amendment in the House Labor and Industry Committee and sent to the House floor by a unanimous vote.

Rep. John Galloway, the prime sponsor, called it "a good first step" toward preventing illegal immigrants from taking jobs that should go to workers who are entitled to them.

The bill, similar to a measure that was scuttled in 2010, would require public contractors and subcontractors on projects that cost at least $25,000 would be required to verify employees' Social Security numbers through federal systems such as E-Verify.

"It's about fairness. It's about jobs," said Galloway, D-Bucks.

Meanwhile, in the Capitol Rotunda, participants in rallies organized by the Pennsylvania Immigration and Citizenship Coalition delivered a letter to lawmakers from dozens of Pennsylvania faith leaders, saying that such bills won't fix a broken immigration system and don't protect community safety or trust.

Tamara Jimenez, a native of Nicaragua and organizer for the New Sanctuary Movement of Philadelphia, warned that an E-Verify mandate could hurt the ability of many small businesses to function. She said many small businesses, like the one run in Philadelphia by her mother and stepfather, are started by immigrants.

"We are not here to take jobs," Jimenez, 24, said. "We are here to provide jobs."

The American Civil Liberties Union of Pennsylvania opposes the legislation because of past accuracy problems with the E-Verify system and because it provides the infrastructure for a national identity system that could be vulnerable to identity thieves.

Andy Hoover, the group's legislative director, cited Galloway's description of the bill as a first step as evidence that supporters would seek to widen its scope in the future.

"That could be the opening of a broad E-Verify mandate and that could be a problem for workers and the business community," he said.