WASHINGTON — Fuzzy math, Illinois State University’s president called it. “Political theater of the worst sort,” said the University of Washington’s head.

President Barack Obama’s new plan to force colleges and universities to contain tuition or face losing federal dollars is raising alarm among education leaders who worry about the threat of government overreach. Particularly sharp words came from the presidents of public universities; they’re already frustrated by increasing state budget cuts.

The reality, said Illinois State’s Al Bowman, is that simple changes cannot easily overcome deficits at many public schools. He said he was happy to hear Obama, in a speech Friday at the University of Michigan, urge state-level support of public universities. But, Bowman said, given the decreases in state aid, tying federal support to tuition prices is a product of fuzzy math.

Illinois has lowered public support for higher education by about one-third over the past decade when adjusted for inflation. Illinois State, with 21,000 students, has raised tuition almost 47 percent since 2007, from $6,150 a year for an in-state undergraduate student to $9,030.

“Most people, including the president, assume if universities were simply more efficient they would be able to operate with much smaller state subsidies, and I believe there are certainly efficiency gains that can be realized,” Bowman said. “But they pale in comparison to the loss in state support.”

Bowman said the undergraduate experience can be made cheaper, but there are trade-offs.

“You could hire mostly part-time, adjunct faculty. You could teach in much larger lecture halls, but the things that would allow you achieve the greatest levels of efficiency would dilute the product and would make it something I wouldn’t be willing to be part of,” he said.

At Washington, President Mike Young said Obama showed he did not understand how the budgets of public universities work.

Young said the total cost to educate college students in his state, which is paid for by both tuition and state government dollars, has gone down because of efficiencies on campus. While universities are tightening costs, the state is cutting their subsidies and authorizing tuition increases to make up for the loss.

Obama’s plan would need approval by Congress, a hard sell in an atmosphere of partisan gridlock.

In his State of the Union address Tuesday, Obama described meeting with university presidents who explained how some schools curtailed costs through technology and redesigning courses to help students finish more quickly. He said more schools need to take such steps.