Higher education leaders have dreamed up two big, radical ideas that could potentially rescue the nation’s top public universities from the brink of fiscal oblivion.

Mary Sue Coleman, president of the University of Michigan, thinks they probably won’t work.

First, a bit of context:

I spoke to her Tuesday about her open letter to President Obama, in which she thanks the president for calling an unusual White House meeting this month to discuss affordability in higher education — and she asks him to take the lead in the battle to keep her own university, and others, affordable.

“The onus is now on all of us — elected officials, university presidents, business leaders, philanthropists and parents — to collaborate on effective answers,” she wrote.

It seemed a polite way of saying that the onus is on him. Coleman wants the president to take a leadership role “in elevating the issue and stimulating the conversation” about keeping college affordable — especially public colleges, and particularly for the students who can least afford to attend.

“I think his voice, the president’s voice, will be extremely powerful,” she said.

Coleman envisions the Obama administration leading the states back from their steady retreat in subsidizing public higher education. She thinks it will might take the personal leadership of the president, along with business leaders and other voices, to persuade legislatures that “states shouldn’t abandon their public institutions, because public institutions bring rewards back to the state.”

Coleman is one of several influential college presidents who are taking a stand in defense of the nation’s great public universities as “drivers of social mobility in this country.”

Together, the top eight public universities (arguably, Berkeley, UCLA, Michigan, the University of Virginia, the University of North Carolina, the College of William and Mary, Georgia Tech and either UC San Diego or Davis) educate many times more students than the eight members of the Ivy League.

“The privates are wonderful, but they’re small,” Coleman said.

The top publics, she contends, play an outsize role in preparing the next generation of leaders — and in keeping the nation competitive with ambitious higher-education agendas in other parts of the world.

“The Asian universities, it’s going to take them a while, but they’re going to catch up,” she said.

But states spend, on average, about one-fifth less per public college student than they did a decade ago. That, in a nutshell, is the root of the funding crisis that is gripping public higher education. State subsidies used to rise from year to year, and in a fairly predictable fashion. Over the past decade or two, they have zigzagged up and down — mostly down.

The collapse of state support to the University of Michigan began earlier than the retrenchment in most other states, because of the decline of the auto industry and overall malaise in the local economy. UMich has coped with an orderly retreat in state subsidies, phasing in tuition increases and cutting administrative costs over several years. The University of California system, by contrast, “dropped off a cliff,” Coleman said, sustaining massive cuts in 2009 and 2010 and raising tuition by one-third in a single year.

Michigan once ranked among the top five states in higher education support. It has dropped to 38th, Coleman said.

“We’ve lost a billion dollars in funding for higher education over a decade,” she said. “We’re not going to get it back in a year.”

There are no quick fixes. But leaders of academia have proposed bigger, long-term changes that could fundamentally alter the way top public flagships are funded.

Here, then, are two of those Big Ideas, and why the president of this top public Ivy doesn’t believe either one can fly.

1. Federalize the flagships.

In a 2009 op-ed in the Post, Berkeley Chancellor Robert Birgeneau proposed a new, hybrid model of funding for the very top public universities.

He suggested that “a limited number of our great public research and teaching universities receive basic operating support from the federal government and their respective state governments.”

The idea was that the federal government would step in to stabilize eroding state support for the schools whose academic output is most vital to the nation’s future.

But Birgeneau’s plan focused only on the elite, and, perhaps inevitably, it came to be seen as elitist. What about all the other public universities, the ones whose overall reliance on state funding is far greater than Berkeley’s, or Michigan’s?

Federalization would certainly help Michigan. The university has absorbed “a 40 percent cut in state aid over a decade in real dollars,” said Philip Hanlon, Michigan’s provost.

The state appropriation has dwindled from 78 percent of Michigan’s budget in 1960 to 17 percent today.

UMich has raised tuition steadily to bridge the gap, and the university has found enough operational “efficiencies” to trim more than $200 million from its annual budget.

An infusion of federal dollars could rescue Michigan from further cuts. But Coleman thinks it’s politically unfeasible.

“If there were a way to get a serious discussion of this issue, count me in,” Coleman said. “I try to think, though, about how you would get that through the current Congress. And this is probably a nonstarter.”

2. Enact progressive tuition

The top private universities have adopted massive need-based aid programs that effectively charge tuition on a sliding scale according to each family’s ability to pay.

The same system is creeping into public universities. Michigan, Berkeley, the University of Virginia and their peers already charge double or triple tuition to out-of-state students and admit them in comparatively large numbers, using their wealth to subsidize the cost of educating everyone else.

All of those schools have enacted large tuition increases over the past decade. But typically, some large percentage of that tuition revenue is recycled as need-based aid, and students from needy families pay minimal expenses to attend.

Presidents, faculty groups and others have proposed various ways of taking this progressive fee model further: allowing the top flagships to set higher tuition rates than other schools, and reinvesting ever larger sums into need-based aid.

At least one prominent public university, Miami University in Ohio, has attempted progressive tuition, setting one high rate for residents and non-residents alike and then awarding scholarships to state residents in proportion to their need.

It didn’t work. Miami University quietly reverted to a traditional structure of (lower) resident and (higher) nonresident tuition.

Tuition increases are not popular. Voters and lawmakers in Virginia, California and other states have protested double-digit tuition increases. Needless to say, state legislators might have a hard time lining up behind a proposal that would effectively double or triple the price tag of a public university.

“I don’t think politically, even though we have constitutional authority in Michigan, that I could charge $36,000 to the richest of students,” Coleman said. “There’s a political dimension here . . . You could make the case that it would be fair. But I think that’s a big stretch.”