For the OP . . . yes it will hurt to have Cs in math and science, especially if these grades are in your junior year. That doesn't mean all is lost, but you are facing an uphill battle because there are lots of applicants who are great all around AND earned As or Bs in those same classes.
If you've already earned the C, it is what it is and you simply have to put your best package together. If you're made real efforts in math and your teacher will write a glowing evaluation, that will help. A high math SAT/ACT also helps. Getting As in other subjects and in other math/science classes helps. Also, if you need to work to support your family or are going through a serious illness in your family, that could be countervailing. Finally, there may be other elements of your application that overcome that blip.
If you are still in school this year (such as that is for most folks), can you drop to non-honors and potentially raise your grade?
A single C won't take you out of the running
Actually, it can. Had it happen to a candidate who was not admitted due to a C+ in AP Physics. Good news is that the candidate reapplied, was accepted, and graduated at the very top of her USNA class. The said, one C -- or even a couple -- is not necessarily fatal. As has been described elsewhere and summarized above, USNA uses a Whole Person/Candidate Score that looks at many things about candidates.
For others reading this who are considering USNA (
this does not necessarily apply to the OP), if you struggle with a subject, do NOT take it as honors/AP/IB. Go with the "normal" level and get an A. If a subject comes easily to you, then challenge yourself with the more advanced level.