“Twenty-five years ago my dream was to drive a motorcycle, but dreams change,” said Mr. Guaman. “Now I just want to feel what it is to drive a car. I’m 44, I never had a chance.”

Mr. Guaman, who is from Ecuador and works in construction, said he first tried getting his license in New York in 1999. One particularly difficult hardship for him has been trying to visit his uncle in Yonkers using only public transportation.

But if he gets a license, Mr. Guaman has a farther destination in mind.

“Get a car and go to Disneyworld,” he said.

In sharp contrast with the enthusiastic attitude of those seeking licenses, the state’s new law continued to be met with resistance from county clerks in conservative areas upstate who oversee Motor Vehicles offices and who have said they would refuse to issue licenses.

The clerk in Rensselaer County, Frank Merola, said on Monday that his office would not be accepting applications from undocumented immigrants, arguing that his employees did not have the training or expertise to determine if foreign passports were legitimate.

“In all the years I’ve been here, we’ve never taken foreign documents,” Mr. Merola said, in an interview. “Now they want us to stand at the counter and make a judgment.”

Mr. Merola, a Republican, said his decision was practical, not political. Those wanting to apply in Rensselaer were being sent to a larger office in Albany, he said. Officials at that office seemed to be ready to process applications, with two employees greeting customers at the door.