But cutting military spending, like any other deficit reduction measure, will only result in an economic downturn. Deficits are not inherently bad; they make up for drains on circulating currency to private savings and net imports. Cutting spending on the military (or on "entitlements" or anything else) reduces the deficit without changing the dynamics of the private or external sectors. This will absolutely lead to higher unemployment, which also means additional expenditures on unemployment and welfare programs, which adds more spending than the cuts removed.
This is what Greece is facing, forced on them by the Troika and their own insistence on staying in the Euro. There may be some structural spending problems in Greece, but the solution is not to cut spending as they have been forced to, but rather to spend as much or more in wiser ways - ways that build the future productivity of their nation. But they chose to relinquish their power to issue currency and must, until they reclaim it, play by the Eurozone rules.
If America wants to avoid Greece's fate we must, first and foremost, avoid misunderstanding the existing realities. Neo-liberal (and even Keynesian) economists slip into traps of worrying about the deficit. But, if we want a growing economy, the deficit must be determined from the private and external sector balances. Any attempt to act directly on the deficit (i.e. cutting spending or raising taxes) is actually self-defeating.