The answer to this question seems rather obvious: those who get such education. Who loses? That is less obvious, and education has positive externalities on others.
Ana Balcão Reis says things are not that simple. First, we have to keep in mind that only few people are credit constrained when it comes to college tuition. Indeed, most of those who are do not make it that far in the first place. Second, those who benefit from public higher education are also those who pay the most taxes, thus the welfare benefit for them is ambiguous. To sort this out, the paper builds a model with different levels of education and agents differing by ability, human capital and the capacity of their parents to pay (which depends on their own human capital).
First think about the marginal agents, those who are the last one to go to public university. They would prefer not to have this option, that is, have only private universities and not pay the associated taxes. But because they have to pay them and college is now cheaper, they choose to get educated with little benefit. Those who do not go to college do not to pay taxes and would thus vote against public higher education. And the richest pay more in taxes than what they would pay in tuition. So all those left in favor of public universities are the not too rich who would go to college anyway. The question is whether they are a majority.
There is one important aspect missing in this analysis, though. Higher education has a positive externality on others: a more educated workforce raises everyone's productivity, and it makes it also easier to accumulate more human capital. This is only partially prices into wages, thus higher education needs some subsidies to reach efficient outcomes. Thus, a microeconomics analysis as performed here misses potentially important macroeconomic effects.