I worked overtime for years. And I was the boss. You do what ya gotta do...
So either you had a very small business with minimal additional human resources, or you were a poor manager (that last statement is NOT intended as a personal insult). Good managers can afford to take time off, as they have trained their people to be able to handle things, even tough things, at least temporarily.
FEMA is certainly not short of human resources. Suppose the guy dropped dead of heart attack or stroke?? I suspect that would be worse....