Republicans tend to take an approach to higher education overhaul that does not expand the size and scope of the federal government, instead arguing for colleges and universities to reduce their operating costs. “Her argument basically is, ‘Let’s just raise taxes and pour more money into the same system,’ ” Mr. Rubio said in an interview. “My argument is: We need a brand-new system.”

Since 2004, tuition and fees for in-state residents at public colleges nationwide have increased 40 percent, adjusted for inflation. State higher education spending per student, adjusted for inflation, dropped 20 percent since 2008 — tipping the balance so that students now pay a greater share of the costs than the states. In bad times, states often use their higher education funds as the balance wheel to keep their budget in order. Some governors, like Scott Walker of Wisconsin, a Republican presidential candidate, have found higher education spending cuts an alternative to trims from Medicaid or the prison system.

To balance their books, most flagship state universities are admitting more out-of-state and international students, who pay much higher tuition.

Though states would be eager for added federal funding, George Pernsteiner, president of the State Higher Education Executive Officers Association, said, they are likely to be wary of giving up their education budget flexibility unless there was a safety valve allowing education reductions in tough economic times.

One fundamental question about Mrs. Clinton’s plan — already raised by several Republicans — is whether it would help cut college costs. A July report from the Federal Reserve Bank of New York concluded that more federal loan money did indeed contribute to higher prices. But last year, a Congressional Research Service report reached the opposite conclusion. And previous studies have gone both ways.

“To prove that X causes Y, you need research that consistently produces the same results, and we haven’t had that,” said Terry W. Hartle, senior vice president of the American Council on Education, the umbrella organization for colleges and universities. “And we think the New York Fed has serious methodological shortcomings.”