Noahpinion recognizes a problem that probably familiar to readers with kids in high school–the high cost of college:

While college enrollment rates are up a little over 50% since 1980, the price of college is up by over 1000%.
What this points to is a supply shortage…
More people want to go to college (probably because of the higher college wage premium), but the supply of high-quality colleges simply isn’t that big. People are flocking to for-profit colleges because there just isn’t room at public ones. And since there are good theoretical as well as empirical reasons to believe that for-profit universities just can’t deliver the goods, the key fact of U.S. higher education would seem to be the stagnant number of spots at good universities.

His solution? National public universities:

Which brings me to my idea of the day: A federally funded National University System.
When you have a supply shortage, one solution is to shift the supply curve to the right. Sometimes this is impossible. But in the case of U.S. public universities, it is very doable! Plenty of other countries have national university systems, and these national universities are often very high-quality. Why not us? Why don’t we build a system of high-quality, federally funded national universities to co-exist alongside our already excellent state universities?
It’s not as if we don’t have the resources to do this. Land is not an issue. And academic jobs are in notoriously short supply, meaning that there is a huge pool of qualified PhD’s ready to teach and do research. We bring the best and the brightest to get PhD’s here, and then a bunch of them end up returning to India, China, or Korea…why not keep more of them here as professors?
As for Constitutional objections, note that we already have a number of federally funded universities.Ever hear of West Point?

One question I have is perception by students: would students want to attend certain universities if they weren’t selective anymore? People want to attend elite universities because they’re hard to get into. Of course, this doesn’t mean we should add more capacity.
And, at least in the sciences, there’s one issue that would make implementation difficult–research. Noahpinion:

And the spillover benefits from more top-quality research universities are potentially enormous. The U.S. depends on innovation and research for its prosperity, and yet federal spending on research and development has fallen by two-thirds since 1960, leaving private companies to pick up the slack. There are plenty of research activities that universities do that private firms can’t, especially basic research. If the U.S. is to remain the world’s technological leader, a National University System would seem to be a good move.

This is where I disagree. Unless these universities were to have positions that also provided research funding, even more science faculty would be competing for the same-sized pool of grant funds. This wouldn’t lead to more research in the science. So either these public universities would focus on high-quality undergraduate instruction and not be research institutions*, or the universities would supply research funding.
Nonetheless, national universities would be a good idea.
*Obviously, some funds could be made available to promote undergraduate research (which works better for some disciplines than others).