Most of it's already paid for, or appropriated for. The military members are already being paid, the equipment and supplies, weapons, and ammo, are already there for an initial conflict. The only additional cost would be transportation and set up of the bases of operation. Again, the equipment would already be in inventory for an initial operation, and further operations would require further appropriations.
I find disgusting that every time the government closes, the government “workers” are retro-paid...giving them yet more paid vacation. This ALWAYS happens. RIF these parasites-with-attitude.