I would disagree. Quite a few polls out there showing that people do not favour increasing military funding;
https://www.salon.com/2017/03/23/the-public-favors...
http://time.com/4253842/defense-spending-obama-con...
http://thehill.com/homenews/administration/322975-...
This one comes closest to supporting your argument, but still only shows 37% as thinking military spending is too low, so I think it's fairly clear that the majority do not want it;
http://nationalinterest.org/blog/the-buzz/new-poll...
Leaving aside the various biases of such polls, more importantly those polls do not reflect the view on the hypothesis that you posited, which is that more Americans would prefer to have free tertiary education over increased military spending. What I was saying was, if you pit those two against each other, I suspect the military spending wins. Much along the lines Trump won over Hilary, despite what the polls said.
The polls don't specifically answer the question I have put forward, I could not find a poll that did, but I think the general results of these polls indicate that I am likely correct, on the balance of probabilities.
The polls I've posted say that most americans are not in favour of increased military spending, and certainly not at the expense of other departmental spending, including education.
If they don't want to cut spending on education to spend it on military instead, then I'd hazard a guess that they would prefer to spend more on education, rather than more on military, as well. I don't think that's much of a jump to take, especially with what looks like an absence of evidence against it.