If it can be postponed indefinitely, then it probably isn't that important. When something is expected of us, if our effort is needed, we strive hard to measure up. Deadlines define what is required of us. If we have deadlines, we either respond or we don't. That is better than not being needed or not having a worthwhile task to do.
Work is sustained effort toward a worthwhile goal.
People can have deadlines and still feel unhappy and unimportant. This happens when the deadlines that are imposed upon them do not reflect their personal aspirations. People do hard things and go through hard times simply because they have to. Uninvited troubles and problems can be just as powerful as the ones we choose for ourselves. Life is such that there are plenty of challenges and problems to go around, even if we don't choose them.