You know, I still don't have a good idea of what the NAP is because everyone who espouses it doesn't articulate their views on what it means very well. I listen to podcasts, ask around, looked it up in wiki. Still doesn't make sense to me.
But I tend to argue well, and one thing I've found is that you make a point to your strengths, and not your weaknesses. If you're going for the NAP before your family can wrap their heads around smaller government, you might as well be debating in different languages.
My suggestion is to instead chip away at the basis of their own belief systems. If they're conservative, ask them who has to pay for a massive military. Keep pounding on it, because if they think conservatives are for less taxes, they shy away from having to explain why were spending money on a military presence in Italy, and the Philippines. If they're liberal, ask them if its racist to give money to individuals on the basis of race. Ask them if they're marginalizing white people from society. Again, peck away at the weak points of their own belief systems at the points where its difficult to defend.