There are two issues here -- scores good enough (so to speak) for USNA and scores good enough for a nom.
USNA states that a good minimum starting point is 600/600. Yes, you can be admitted with less and a good number of students are. But if you have less than that, you should definitely retake the SAT or try the ACT, if you can financially afford to do so. And, as another poster said, it pays to study before retaking.
Competitive scores are typically low 600s verbal and 650+ in math. However, in some competitive geographic areas, that may not be enough to get a nomination from your MOC.
I suggest you discuss your scores with your BGO, who should have a good idea of what typically is needed in your area. And, as noted above, there is a LOT more to your application than just your scores. They matter, but they aren't the only thing that matters.