National defense exists in very few nation states today. National defense implies that your forces are strictly defensive. Why would you need several aircraft carriers, hovercrafts, and other equipment when you already have a nuclear arsenal that could render the Earth uninhabitable, and when you have anti-missile systems that can shoot satellites out of orbit? The nukes and the anti-missile systems should realistically be enough to destroy any army, navy, or air force. Having a few nukes and a few missile defense systems wouldn't be anywhere near the cost of a massive force of men and massive amount of machinery.
Of course, people would not buy these things individually. A company would build these things, and then offer protection plans to people within neighborhoods and/or cities. Should enough people in each neighborhood or city wish to have such protection, then such protection would be provided. If the payment threshold is not reached, no one has such protection. If people truly value such protection, it would stand to reason that it would be provided. This same strategy works for small armed groups protecting cities/neighborhoods.
Private security already exists for corporations and large businesses. Private militaries are already contracted by governments as well. If the government went away, these groups would still want to make money.
Some people fear that these groups would become governments, but I disagree. Right now, they earn quite a bit of profit by being paid and not having to actually use their equipment. If such groups tried to take over a given geographic territory they would need to spend quite a bit of money to do it. War is not cheap, and so the American military which has been consistently active for quite some time now requires quite a bit of funding.