Other groups, including , a conservative Washington D.C.-based public policy research group, and have also pushed for the use of E-Verify.

Others, however, said that mandating the system's use in the stimulus package could create problems for both employers and employees -- and could slow the deployment of much-needed infrastructure projects.

Mike Aitken, director of governmental affairs at the Society for Human Resource Management (SHRM), a trade association in Alexandria, Va., said his group is not opposed to having an efficient and accurate employment verification system. But its use now could unnecessarily delay "shovel-ready" projects.

Many state and local governments that would participate in the program are currently not signed up for E-Verify. Requiring each of them to sign up now, and roll out new processes for procuring workers and checking eligibility, would be needlessly cumbersome, he said. And he expressed concerns about how the system would respond if that number were to increase dramatically as a result of a mandate, Aitken said.

"We don't think E-Verify can handle the massive influx of employers in such a short amount of time," he said. "We don't think it is ready from a capacity standpoint. It will take time to get the system up and ready."