The program to provide free tuition for students at New York State’s public colleges and universities passed on Friday by the Legislature has been hailed as a breakthrough and a model for other states that will change the lives of students at public colleges across the state.

The Excelsior Scholarship, as the program is called, is expected to cut the cost of a degree from a four-year State University of New York college — now almost $83,000 for tuition, fees and room and board — by about $26,000 for an eligible family making $100,000 a year. That is a substantial reduction, but still means paying about $57,000 over four years.

And it was met with accolades from, among others, Hillary Clinton, who posted on Twitter: “Let’s celebrate New York State getting something important done that we wanted to do nationally. A great step for progressives.”

The program, which Gov. Andrew M. Cuomo made a legislative priority, will primarily benefit traditional students, those who go to college straight from high school and earn their degrees on time. The state’s college students, increasingly, are not like that. Many of them attend part time and take extra years to earn their degrees, so Excelsior will not help them.