Alabama GOP Sen. Jeff Sessions agreed, arguing that America has "more low skilled labor than we can find jobs for today."
"I think this (fact was) not considered properly in this bill," said Sessions, who declared that the legislation was written by "big business" and "big agricultural interests."
But Douglas Holtz-Eakin, a leading GOP voice on economic issues and former head of the Congressional Budget Office, insisted that illegal immigration isn't the main problem for the country's low skill workers.
American workers with few skills are being forced to compete globally, he told the panel. "Geographic location has very little to do with it."
Legalizing undocumented workers will help "eliminate the capacity for exploitation," he added.
Under the bill, most undocumented immigrants who arrived in the United States before December 31, 2011, would be eligible for legal residency and ultimately citizenship. They cannot, however, have any felony convictions in U.S. or foreign courts.
Smaller offenses can also block residency. The bill would block applicants with more than three misdemeanor convictions, including for offenses such as reckless driving, trespassing or vandalism.
The bill would also require undocumented immigrants to pay a penalty of up to $500 for having come to the United States illegally, and also pay any back taxes before receiving temporary approval to stay.
After 10 years as provisional residents, immigrants could become lawful permanent residents by following the same guidelines as immigrants who enter the country legally. That process includes a $1,000 fee.
The Judiciary Committee is set to hold another hearing on the bill on Monday. Full Senate consideration would likely occur in June, according to multiple sources.
A bipartisan group of legislators in the House of Representatives is crafting its own immigration reform proposal.