The java.util.Timer effectively does what your colleague suggests (truth be told, in the end, there really aren't that many ways to do this).
It maintains a collection of TimerTasks, and it waits for new activity on it, or until the time has come to execute the next task. It doesn't poll the collection, it "knows" that the next task will fire in N seconds, and waits until that happens or anything else (such as a TimerTask added or deleted). This is better overall than polling, since it spends most of its time sleeping.
So, in the end, you're both right -- you should use a Timer for this, because it basically does what your coworker wants to do.