Luis Jimenez, 33, another dairy worker who said that he drove without a license, said: “We are workers. We are not here to harm anybody. We need things to advance.”

Supporters of efforts to allow those who are undocumented to get driver’s licenses say that public safety would improve because they would be required to pass road tests and obtain insurance. But critics said that licenses represented a privilege that unauthorized immigrants should not hold, because they should not be here in the first place.

Outside of Rochester, Tony Bartolucci, a pastor, and his daughter were struck by an unlicensed, undocumented driver on their way to buying a Christmas tree on Christmas Eve in 2015. His daughter, Giana, 14, died six months later after brain surgery.

“It was the second time that he was caught in the country illegally,” Mr. Bartolucci said. “And both times were due to his being drunk while driving. Obviously, if he wasn’t in the country illegally, it wouldn’t have happened either. But I’m not going to make a political point about it.”

He believes in restricting illegal immigration and thinks that giving driver’s licenses to people in the country illegally is just “a non sequitur.” But at the same time, Mr. Bartolucci said, he has forgiven his daughter’s killer.

While Connecticut and Vermont enacted laws in 2013 that allow noncitizens to obtain licenses, a similar effort in New York has made little progress in more than a decade.

Image Giana Bartolucci died after her father’s car was struck by an unlicensed, undocumented driver on Christmas Eve in 2015.

In 2007, Gov. Eliot Spitzer ordered that unauthorized immigrants be given licenses, but within two months, he was forced to rescind the order under pressure from upstate county clerks — serving as officers of the Department of Motor Vehicles — who refused to enforce it. Bills supporting the idea have been introduced in the State Assembly the last three years, but in June, another legislative session ended without a bill for “limited purpose drivers’ licenses” getting out of the transportation committee.