The straightforward way to find the difference in time is to simply use Date().getTime() for time in milliseconds. Just subtract the current date in millisecs from the future date in millisecs. It may also possible to use Calendar.add() to find the difference in time.
I have two suggestions for keeping the information out of the way of your workspace.
You could make a program that updates the frame title with the message (i.e. 2 days left). This app doesn't have to have a visible frame, or the app could start minimized. This is probably the easiest out-of-the-way approach for a countdown timer.