Junior/Senior year of engineering school is hard to juggle with anything. That said, it is not impossible and though it may sound cheesy, is "character building" IMHO. I am just finishing an 18 credit term (of very challenging senior year engineering classes) while also holding a senior billet in my Battalion. It has probably been the most difficult term of my college career, but it IS doable. Being organized helps, and learning to prioritize is the real key.
I will say that in the past I had felt engineering involved about the same amount of work and difficulty as a liberal arts degree, just in different ways. Now I would venture to say that it IS a lot harder. My point being, do engineering because YOU want to, not because you think the Navy wants you to. It will not be a walk in the park, and all the Navy really cares about is whether or not you get a degree. So choose your major wisely.
All of what JAC said above is good stuff, here's my take on an engineering degree that I got almost 5yrs ago:
An engineering degree isn't the easiest degree to get. It takes a lot of hard work, time, and determination. Sure, you might not party as much as your communication major buddies, but majoring in engineering isn't necessarily going to turn you into some nerdy hermit. It's very possible to do NROTC, be an engineer, party, and do some other things with your college life. Like JAC said, it's all about time management.
Since I left grad school, I haven't touched my engineering skills. Having an aeronutics back ground in no way gave me a leg up when it came to flying. But, getting an engineering degree did give me excellent academic confidence, a comfort with technical subjects, and time management skills. Sure, I have yet to have to do any partial differential equations in the Navy, but the academic confidence was nice when it came to things like API and flight school tests and memorizing NATOPS.
All that being said, do engineering because you have an interest in it. I'm sure just about any other major can give you the same skills, I stuck with engineering because it was interesting and I enjoyed the challenge.