The big banks got bailed out, and presidential contender Bernie Sanders says they should pay it forward.

The independent senator from Vermont introduced his plan on Tuesday, which would use a tax on stock trades to help pay students' tuition.

The price of attending a public college has been climbing since the 1980s. Sanders's plan would shift the burden to pay for college away from students and families and back onto the government.

Sanders's bill, which he says would cost $47 billion in the first year, doesn't stand a chance in the Senate. But it highlights an important question for higher education policy: can the federal government force states to make college more affordable?

Students are footing a bigger share of college costs than ever before

Public college tuition has risen 30 percent in the past decade. Since 2004, published tuition rates have jumped from $6,448 in 2004 to $9,139 in 2014.

Net tuition at public colleges — the amount students actually pay after financial aid is taken into account — has, meanwhile, nearly doubled since 2000.

Part of this is a story about rising tuition costs, as the price to attend both public and private colleges has grown rapidly in recent years. But there is a second story here, one about states' funding for higher education not keeping pace with all the students who want to attend — and leaving students to pay a bigger chunk of their bill.

In the late 1980s, only about a quarter of public college revenue came from tuition. The rest came from the state or other sources. Now students cover about half the cost of their education — and may soon provide the majority of public college revenues.

In general, public colleges spend about the same amount per student that they did in 1987. States are spending more on higher education than they did in the past. But more people go to college than used to, and state budgets haven't been able to keep up with enrollment increases and inflation.

Students at public universities are now increasingly likely to borrow, and more likely to graduate with debt: 59 percent of students at public colleges took out loans in 2012, and students who borrowed graduated with an average of $25,600 in debt.

Sanders's plan requires states to spend more on education

Sanders's plan would set up a grant program to cover the share of tuition that students currently pay. The federal government would pay for two-thirds of the grant program's budget, using a new tax on stock trades to raise an estimated $47 billion in revenue.

States would be required to chip in the additional one-third of funding, as well as keep up their current spending levels on higher education.

While Sanders's proposal is far to the left of many Democrats, the type of grant program he proposed isn't totally different from other proposals floated on Capitol Hill. Requiring states to fund higher education has been tried before, and it worked.

The 2009 stimulus bill barred states from cutting higher education funding below 2006 levels. If they did, they'd lose all federal education funds. Over the next two years, states cut right up to that threshold — but they didn't go over it. The more dramatic cuts were made after the stimulus provision expired.

Strengthening the Education Department's oversight role

Sanders's bill, though, wouldn't just increase the amount the federal government spends on higher education. It would give the Education Department much more leverage over states' higher education policy.

The Sanders bill would also require public universities to employ tenured or tenure-track faculty to provide 75 percent of their instruction — an attempt to reverse a shift toward using more part-time and adjunct faculty to teach classes, which has become an important higher education labor issue.

That's why, as much as public colleges would appreciate the extra funding, they also might be wary of a proposal like Sanders's. By paying the bills, the federal government also buys itself more influence.