I've always been very lucky in that at each of my jobs I've had the lattitude to make those decisions. I've been able to make those decisions - relatively on my own - because I maintain excellent communications with program and other staff so that I always know organizational needs and wants. As I'm doing research or as opportunities arise, I'm generally able to take advantage of them because I'm always abreast of what's going on funding-wise and organizationally.
Remain calm and try to gauge the situation, always pointing out you're willing to help but not to the point where you jeopardize your other tasks. If they prove to be too difficult, then seek advice from higher.