The nice things with this is whatever it is that matters most can vary considerably. For one character, it could be a life or death situation. Another character could be terribly worked up because they're late back with their library book. The potential for humour is here too.
The one proviso is that your characters have to have very good reasons for why these things matter. A life or death scenario has an obvious "why it matters" inherent in it. In the case of the library book scenario, could it be that your character has never been late in their life for anything and fears losing control over their neat little life if they ARE late at all? Maybe they worry about what the librarian will think - other people's opinions matter to this character. You get the idea.
Have fun and play with this. Work out what could make your character lose what matters most. For someone with a controlled life, what on earth has happened to make the possibility of being late back with their library book happen at all? Something catastrophic (to them) must have occurred. Hopefully it will be very entertaining for a reader!