I have some tasks that I do every day, and they may take around half an hour on average. If I want to go on vacation and I ask a coworker to cover that task, but they say no, is this something worth escalating to the boss? Or should I just suck it up and do it on my day off since it doesn't take that long. Someone has to do this task every day.
is this something worth escalating to boss?
If the task truly must be performed every day, then clearly your boss needs to find someone else to do it while you are away.
Something like, "Boss, task X still needs to be done while I'm gone. I haven't been able to find anyone who would agree to do it. What should we do?" is appropriate.
For the long term, this is something that should probably be automated if at all possible.
You don't work on your day off. Even if it's only half an hour (exception if there is an absolute emergency that could cause massive damage).
It's your responsibility that all work that has a deadline is done within that deadline. You achieve that by first asking a co-worker, and if they refuse, by asking your manager. If you tell your manager that this work will not be done because your co-worker refuses, then it's in the manager's hand and their responsibility.
When you're on vacation (or in hospital, or six feet under) it's not your responsibility to do that work as you're not at work.
It's also not your responsibility to find a substitute who can do your regular tasks on that day, it's your organization's responsibility to plan for such situations. This includes determining who is able to and will do the work when you're not available.
When you go on a planned vacation, you may tell that person that they will have to do the work as per that prior agreement, and you may tell your boss that you told your coworker, but both of this is actually optional - your boss needs to know what arrangements were made, and they should communicate with your coworker accordingly.
If these regular tasks are not something that your boss knows about, it's about time to tell them - there should not be any important part of your work that is unknown to your boss, exactly for the reasons stated.
Send your manager an email:
Just wanted to give a quick reminder that I'll be on vacation between x-y. The team relies on this task usually I'm handling daily. Please let me know if you need anything from me regarding the temporary handover of this task.
Thanks, and best regards,
Managing your replacement is not your responsibility, it's your manager's. (Hence the name.)
While this may depend on work culture and the exact nature of the organisation, I'd suggest going to your manager first and not approach your co-worker directly. It is your manager's responsibility to make sure your tasks are covered in your absence. It is your duty to make them aware of any critical tasks that must be done within the span of your absence.
Your boss is in a better position to judge whether this task is best done by your colleague, or someone else, since they would know other schedules and workloads, ideally.
It's not your job to find someone to cover your tasks while you're away, it's your boss'. Assigning resources is, quite literally, the only vaguely useful thing that management has to do.
You've been nice by trying to organise it yourself. Since your colleague said no, just tell your boss that he's going to have to find someone to cover it. I wouldn't mention that your colleague said no, just say you've had a quick look (to try and avoid bothering them with it) and haven't been able to find anyone.
Regardless of what is then said, you take your holiday, and don't work on your holiday. Your boss' inability to manage resource is not a reason for you to work over or not take your holiday.