Well, in general, people in our society today are completely removed from death, so imagine if all of a sudden, we all found our death dates. It would be a real slap in the face to humans that death is real.
This could possibly lead to some people being depressed and agreesive, but there are also probably going to be pepole who don't want to accept their death, so they are going to take crazy measures to prevent their own death.
I guess I didn't directly answer your question, but that was just to get some of your creative juices flowing. I know it seems hard to come up with plot point ideas, but this story idea itself is pretty creative, so I think you can do it :). Just keep asking yourself "What if?" Questions and you'll eventually find d your plot.
Good luck and happy writing :)