I'm not sure where this would fall since it's not exactly an impossible request yet it's not quite a demand for loyalty either.
A little over a year ago, we had four employees (including me) handling a task that has many steps and takes a long time just to do once (four employees were handling it because we often have multiple requests for this task to be done -- at this time, it's about 15-20). Since then, one person retired (not replaced), one went on sick leave in December and one went on sick leave this month. While a temp was brought in for the one who went out in December, University policy does not allow her to do a major part of this task because it requires access to an application for which she's not allowed clearance. Anyway, I am the sole person handling this these steps of the task for 2-3 months (these steps, overall, take about 3-3.5 hrs per request) . On top of this, the temp was approved to work the same special schedule CW had, which means working 8 9-hour days, 1 8-hour day then being off every other Friday. The problem is that Temp doesn't work the 9th hour during office hours when she would be needed, she works it when everyone is gone so she has nothing to do. She also doesn't have the tasks down like CW did so she really is needed to be available everyday.
OTOH, I.am.SWAMPED. I am so busy that all my work is behind. I finally determined that I wasn't going to stress myself out trying to get everything done and working from home because management has made such an incredibly stupid decision so, when the main phones are ringing off the hook because I am on the phone trying to cover an emergent situation, I'm just going to let them ring because there are three other individuals who are phone back-up (two of whom are responsible for Temp getting this special schedule). When I was told Friday that we were out of toner for one of the printers, I said Temp would need to order it on Monday. Coworker (who gave Temp the idea of having the special schedule) said to me, "It needs to be ordered today." I told her, "I don't have time to deal with supplies today" (totally true -- it took me, literally, one week just to finally get to review an order I was doing, and I only finally got to it because it was the last possible day I could do it as the order was for the weekend). I've stayed late (making me cancel other income-earning opportunities in order to accommodate my job), my house is a bigger mess than usual (because I'm exhausted by the time I get home from my regular job) and I've worked from home to try to get caught up. I've had enough. I'm ready to argue my points should someone complain to my supervisor about things falling behind (I haven't complained to my supervisor more than expressing concern about the special schedule because I know now is not a good time -- at best, he'll blow me off and, at worst, he'll blow up at ME; however, if someone else should bring it up, I'm ready to present the cause for things being this way).
The toner cartridge request seems like a such a small thing on its own, but there has been one after another of these "small things." I feel that the others need to feel exactly what happens if the person who handles these things isn't available because they gave her a stupid schedule. It shouldn't impact my workload (seriously, it would've further pushed back my other work, which no one but me could get done). I was also at lunch when this request came through so I wasn't paying attention after I gave my "sorry, not going to happen" line; I saw the two individuals responsible for the stupid schedule running around trying to fix the problem. I'm still pretty mad and just wonder "Really? Your poor planning should constitute an emergency on MY part??? NOT!"
So, my response to my "impossible" patron request (of magically coming up with time to take care of that which would be taken care of by the Temp if she were working on Friday like she really is needed to be) is "I'm not going to stress myself out and cause detriment to any part of my life anymore because of YOUR poor planning; do it yourself or wait until the Temp is available on Monday."