The military has enjoyed recruiting success lately, despite the rather vivid risks associated with "travel" to Afghanistan and Iraq.
I see several interpretations of this observation:
Private spending has fallen, and is an important determinant of total labor demand. Lots of people are looking for a public sector job, and the military is a natural public sector destination for young people.
The composition of private spending has changed from consumption to exports, and young people have a comparative advantage in retail activities. Thus, their effective private sector productivity has fallen (even while productivity has risen more generally), and they are shifting to the military
The federal minimum wage is especially binding for young people that might work in the private sector. Even if we ignore the fact that the law dictating that minimum wage does not apply to military salaries, it certainly applies only to PECUNIARY pay. For example, if an employer paid young people $20 per hour in money, but exposed them to $19 per hour in bad-working conditions (safety risk, time away from family, early morning bugle calls, etc.), the net wage of $1 per hour is perfectly consistent with the federal minimum because it applies to the $20. Thus, even if aggregate labor supply shifted in, the military would enjoy a relative employment advantage because of the composition of its compensation.
Some other labor market friction (search, perverse employer incentives, student loan modification with special provisions for public sector employees, etc.) does more harm to private sector employment than to military employment. Thus, as in (2) above, the military is seeing its part of the reallocation of labor from private to public sector.
Obviously, some who call themselves "Keynesian" would stop at (1), despite the lack of a coherent explanation for their spending-employment hypothesis that meets the facts about supply shifts during this recession. I tend to think it is a combination of (2) and (4), but in any case the causes of this recession may be most visible in the market for young employees.