You would expect countries with a higher per capita GDP to spend more on education, and they do. In fact, a graph that plots the relationship across countries between per capita GDP and per student spending on primary and secondary education almost traces out a straight line. But for spending per student on post-secondary education, the U.S. spends far more one would predict based on per capita GDP. Here's the graphs from The Condition of Education 2012, published by the National Center for Education Statistics at the U.S. Department of Education, using OECD data.
First, here's the relationship from per capita GDP to per student spending on primary and secondary education. The U.S. has higher per capita GDP, and accordingly spends more per student, but the relationship is close to a straight line.
Now here's the relationship from per capita GDP to per student spending on postsecondary education. While the relationship remains generally upward-sloping, there are clearly countries that spend less per student than you would expect given their level of per capita GDP, like Iceland, which is labelled, and Italy, which is the unlabelled point more-or-less under Spain. There are also countries that spend more per student than you would expect given their GDP, including Ireland, Canada, and especially the United States.
One can of course make an argument that that the quality of postsecondary education in the United States is very high, which in turn accounts for much of its higher cost. It's a fair point. But for the U.S., the arithmetic of having per student postsecondary education spending so far above the best-fit line with per capita GDP has two difficult implications. First, given these high costs per student, relative to the income level in the economy, it becomes much harder for the U.S. to finance a substantial expansion in the number of students who receive postsecondary education--unless those additional students receive an experience quite a bit less expensive than the current average. Second, the economic payoff to postsecondary education will be harder to justify in the United States, given that the per student costs are so out of line with per capita GDP.