What does a engine coolant warning light mean and how serious is it?

Accidentally ran over a rock in the dark while trying to make a three-point turn. My engine coolant light came on almost immediately. Thankfully I was only a turn away from my driveway and was able to park. It is too late for me to find a garage right now, and I have to work too early in the morning to take it then. Will I be able to drive my car tomorrow after a night of cool down, or should I find alternate transportation until I can take it to a garage?