While this post focuses on universities and libraries, and I'm serious about preferring university cuts to library cuts, obviously there are plenty of other things that could probably be cut first.
I know the answer to this, and it makes me a bit sad. It's easy for Americans to resent their university system because, at least in CS, it is arguable that they don't actually need it. In some cases, it even hurts American kids. But before we all jump on this bandwagon (again) let's consider that we are perhaps being a bit myopic.
In the first place, libraries are a great repository of knowledge. But knowledge does not equal production, and whether you or I or anyone else here wants to admit it, a tremendous amount of stuff has been invented, either totally, or almost totally, as a component of university research. What would the world be without transactional databases, A* search, quicksort, cryptography, the idea of programming languages and so on ad infinatum. I could probably fill up literally a whole book listing the things in CS that were invented at Universities. There are more for other fields. You might contend that they all would have been invented eventually, but the question still remains: what would the world look like if universities had not been around to foster these ideas? New ideas need friends, and Bell labs can't employ all the geniuses.
I know, I know, you might contend that most research in universities is either pointless or close to pointless. Unfortunately, you'd be right. But remember, that's the Zipf curve. The ideas that are big are really, really big. Not just in universities, either: ideas produced by universities (for example, the ones I listed above) have changed the way that the world operates at a fundamental level, and they continue to do this. And when people come to universities and engage in work related to it, they carry it home, they carry it to their job, and they carry it out of the country. This is the way the world works. I know HN hates this opinion, but it is true.
The other thing I want to mention is that the vast majority of these life-changing ideas come out of American universities. This is a truly global system now. People come from all over the world to study here, and when they do, they sometimes stay here. Do people come to America to study at libraries? The simple and fact of the matter is that not all talented people are born in the US, and American universities are a very important gateway to get talented people into the US. In contrast, the library system is a purely domestic product for the public that happens to be inside US. I know that you think that universities don't "help the poor", but consider that this is really only true for the domestic poor. They are an irreplaceable resource for the poor outside. I'm not pitting "our" poor against "their" poor, but it's just something to think about.
The last thing I wanted to point out is that the fact that libraries are a useful repository of knowledge does not mean that it will make people productive. Universities are not good at this either, but the consistent usership of public libraries is pitifully small. The fact that they exist does not mean that people will use them, since they do exist, and people clearly mostly do not.
The bottom line is this: your points all have some grain of truth to them, or they are true outright. But when you don't bother to examine why this system exists to begin with before you state that another systems should be preferred, you are undermining your own point in a huge way. In particular, to say that we should toss an incredibly important and global system for some domestic system that people don't use is utterly wrong. That all said, the correct answer is: cut neither, and instead cut part of the military.