Governor Haslam argued that for students, the importance of his plan is not just economic, but psychological. Students may not be aware that the sticker price of college is not the true price, and explaining the difference can get complicated.

“It is more affordable than most people think, but if they don’t know that, that doesn’t help us,” he said. “If we can go to people and say, ‘This is totally free,’ that gets their attention.”

The cost to the state is fairly low — the governor estimated $34 million a year, paid for by diverting surplus revenue from the state lottery. He said the state would work with private foundations to provide mentors to students to advise them on navigating college.

In addition to its 13 degree-granting community colleges, Tennessee has one of the nation’s most robust systems of vocational schools, the 27 Colleges of Applied Technology, which are a national leader in graduation rates. The governor’s tuition-free plan includes those technical schools.

Mr. Haslam also called for Tennessee’s public colleges to make a new effort to recruit the state’s nearly one million adults who have some college credits but ended their educations without earning degrees or professional certificates. And he proposed expanding a program that gives particular help to struggling high school students so they can go to college without needing remedial classes that do not earn college credit; studies have shown that students who take remedial courses are far less likely to graduate.

Mr. Haslam is one of several Republican governors promoting increased spending on certain programs as a response to growing inequality in incomes and opportunity — an issue more commonly associated with Democrats — that puts them at odds with their party members in Congress. Republicans in several states have moved to expand prekindergarten classes.

But while some of those lawmakers are struggling politically and looking for ways to broaden their appeal, Mr. Haslam, first elected in 2010 and seeking re-election this year, is very popular in his state and has not yet drawn a prominent opponent. In a Vanderbilt University poll conducted Nov. 20 to Dec. 5, 61 percent of Tennessee voters approved of the job he was doing, including 48 percent of Democrats.

California had junior colleges without tuition or fees for decades, and the City University of New York did not charge for either two- or four-year colleges until the 1970s.