The best way to get people to do a job is to pay them enough that they choose to. If people are not choosing to join the army that means they are not getting paid enough. The government has the power to coerce people into doing things and the preferred way of doing this in this case is taxation. Make everyone contribute to the war effort and let the market choose who pays in cash and who pays in risk of bodily harm but is compensated financially.

Hmm. What if the economy can't support the level of taxation required to encourage enough soldiers? There's got to be a point at which this isn't the answer. (Libertarians would say it's the point at which you start taxing people.)