I generally use countdowns for travelling, so I don't have to keep track of mileage to get from A to B. I put interesting landmarks at each tick of the clock, or threat moves that I might consider. Advancing the clock might be a roll, or it might just advance when they say they travel.
I also use countdowns for important people's tolerance of the players. For example, my hardholder King Millions had a countdown before he'd send his gang after the players. Checking off the timer happened whenever they'd question him, or show him up in some way. Or Amy's tolerance of being fucked around by JC (an Operator PC), the countdown essentially representing how many times he can let her down before her heart broke and love died.
Hmm... I've done it for diseases, when tracking how sick a person or group got. Essentially, the whole purpose of countdowns is a pacing mechanism, essentially a barometer for the MC to use so that he can ramp things up in a logical sort of way.
As a suggestion:
The Unwashed Masses Discontent: Advanced whenever something good happens to the holdings. 3pm - grumbling, 6pm - Thrown bricks at hardholds, 9pm - Open threats, 10pm - Gunfire at the hardholds, 11pm - War drums 12pm - open hostility, attacks
With this one, you can keep announcing the future badness. Again, see how it ramps up, each event feeding on the other, again the countdown just keeps it advancing. At each point, there's a chance for the players to get involved, and do something about the situation, before it gets to the end badness. Again, think of pacing.