To be fair, state and local governments would have to increase the total tax burden on their populace to increase education funding, or makes cuts to other things in their domain. The federal government could certainly cut the military budget and grant those funds to state or local education programs, without increasing anyone's tax burden.

That said, my understanding is that the military budget mostly goes to salaries, so any drastic cuts would leave us with massive unemployment. You'd have to take things really slow to make that big a change in the labor force without pretty ugly side effects.