KNOXVILLE, Tenn. » In California, community college tuition and fees average less than $1,500 a year, the lowest in the nation, and with government grants, most students pay nothing. In Florida and Michigan, the cost is more than $3,000, yet poorer students still attend free. But in Vermont and New Hampshire, prices are around $7,000, well over what government grants cover.

That broad range means that President Barack Obama’s proposal to make community college tuition-free nationwide — if Congress and the states were to embrace it — would benefit every student of the two-year colleges, but far greater benefits would go to students in the states with the highest tuition. And while it would aid the economically hard-pressed, it would also effectively extend federal aid to millions of middle- and upper-income students who do not qualify for it currently.

Introducing his proposal here Friday, Obama vowed to make college affordable for all Americans by investing $60 billion over the next 10 years to provide free community college tuition to as many as 9 million students a year across the country. If Congress and the states adopted his plan, the president said, "two years of college will become as free and universal as high school is today."

But even as Obama hosted three Republican lawmakers from Tennessee on Air Force One for the trip from Washington, his adversaries on Capitol Hill showed little interest in signing on to a new and costly initiative that extends the federal government’s reach into education policy, no matter that it is modeled partly on a program created by Tennessee’s Republican governor, Bill Haslam.

Sen. Bob Corker, R-Tenn., who was in the audience after traveling with the president, praised Haslam for helping students pay for community college, but said he did not think a new federal program was the way to go.

"You’re always better off letting states mimic each other," he told reporters before the president’s remarks.

Even if his plan gains no traction in Congress, the president is laying claim to a big idea at a time when lawmakers are planning to renegotiate the Higher Education Act that governs federal financing of college education. Democrats believe that tackling the cost of college is an issue that plays to their strengths — one they can run on in 2016. Still, not all of them were comfortable with the plan.

Rep. Steve Cohen, D-Tenn., questioned Obama’s choice to model his plan after his state’s community college initiative, arguing that the program helps more affluent and lower-achieving students rather than those with the greatest financial need and the best chance of excelling academically.

"He shouldn’t be holding Tennessee Promise out as a model because it’s not a model; it’s a facade to cover up what is a dying system that hasn’t been funded," said Cohen, an architect of Tennessee’s HOPE college program that rewards students for achievement.

Obama’s plan, which states would have to opt into, would not help students at for-profit colleges, widening the cost advantage that community colleges have over the for-profits. It is the latest in a series of steps the administration has taken that would undermine the for-profit sector, whose students tend to accumulate more debt and have poorer job prospects.

Some public four-year colleges, if not the flagship universities, could also see an enrollment drop from such a proposal. Terry W. Hartle, senior vice president of the American Council on Education, the nation’s largest alliance of colleges and universities, said some states might lobby to have four-year colleges included.

Community college is already tuition-free for many students around the country, because the Federal Pell grants for low- and middle-income students cover up to $5,730 a year, and some states add their own grants, while the national average for full-time community college tuition and fees is $3,427.

When Pell grants exceed tuition, students can use the remainder for other costs like books, supplies, room and board. That means if the president’s community college plan were approved, students who could attend tuition-free would be able to use the entire Pell grant for other living expenses, White House officials said. Students would be eligible for free tuition for up to three years, if they attended school at least half time, and maintained a 2.5 grade-point average.

Living expenses are crucial, because most community college students work and attend school only part-time. More than two-thirds hold jobs and one-third have family incomes below $20,000. Studies have shown that no more than one-quarter of students who enroll part-time ever graduate.

Yet the main problems with community colleges, academics say, are dismal graduation rates, and poor preparation for either four-year colleges or the job market — not cost.

"We should be much more concerned about quality and about completion," said Sandy Baum, a senior fellow at the Urban Institute, and a research professor at the George Washington University’s Graduate School of Education and Human Development.

Still, she and other advocates for expanded access to college say the potential financial benefit of the president’s plan is important, as is the powerful message sent by the word free.

"It’s easy enough to say that Pell grants, in most states, cover the whole cost of tuition for eligible students, but I think a lot of students don’t realize that," said Thomas Bailey, director of the Community College Research Center at Columbia University’s Teachers College. "So the publicity, and raising the profile as this announcement may do, is important in getting out the word that the cost of tuition isn’t standing in the way of going to college."

The offer of federal aid to the states to cover tuition costs would come with some strings attached. White House officials said that to take part in the program, states would have to make improvements to community colleges, would have to raise graduation rates, make credits transferable to four-year colleges and ensure that students are learning useful skills.

The Tennessee program, offering tuition-free community college or trade school, shows one possible path to improvement, promising that mentors would work directly with community college students and keep them on track to graduation. The program will take effect later this year, so its effectiveness has not been proved, though interest from 12th graders has been high.

Obama’s plan faces a series of political and practical hurdles, starting with winning approval from a Republican-controlled Congress. Though he said the federal government would pick up most of the tab, the president’s proposal would require cooperation and some investment from state governments — a parallel to the Medicaid expansion in the Affordable Care Act, which 23 states have refused to join.

Obama called for the federal government to pay three-quarters of the cost of eliminating tuition, with the states paying one-quarter. But White House officials said a state-by-state formula would have to be worked out, and it would not be as simple as paying each state three-quarters of what it now charges students, which would reward states that charge the most.

If tuition-free schooling increases enrollment, it would strain the capacity of community colleges in many states; when enrollment swelled during the recession, community colleges in California and other states turned away students.

Ted Mitchell, undersecretary of the Department of Education, acknowledged that in a conference call with reporters Thursday evening, but added, "We think this is a good problem to have."

Michael D. Shear and Richard Pirez-Peqa, New York Times

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