I'm currently dealing with a hostile coworker of sorts of my own, but didn't want to hijack the other thread. In the past, I've gotten along ok with "Lisa" (we've worked in the same department for several years now, until recently on separate but related tasks).
Lisa is basically a nice person, but when she gets stressed or overwhelmed, she tends to lose sight of the fact that I have other duties that are often a higher priority than what she wants help with. This has led to some discussions between us in the past, when she's asked me for help - wanted help immediately - and gotten upset when I told her "no" or "not now." Basically, she seems to think I should drop everything and help her any time she wants it, while my perspective is that, absent an over-riding priority (which mostly there isn't), my work comes first and I'll help out if - and only if - I have time, and there aren't situations in which I would ask her for help. Technically, my position is considered higher in the hierarchy than hers is, but she doesn't report to me.
More recently, there's been some shifting around in my department, and a couple of people have left (voluntarily). This has led to a change in my duties and an increase in workload for most of us. My duties have changed significantly; they now have very little to do with what Lisa does. But twice in recent meetings involving others in the department besides her and me, she has very publicly - and pointedly - asked me to do or help with some tasks. I've declined both times (trying not to make a big(ger) deal out of it and the group has just moved on with the meeting), but I'm now pretty annoyed with her. Her whole tone and body language is very demanding and resentful when she makes these "requests," and the venue she's choosing is not appropriate.
Today (after the second incident), I took Supervisor aside and asked if he could clarify for Lisa that my duties have changed, and that I am focusing on my new responsibilities, and not available to help. Supervisor agreed, but I suspect that this is not the last time this will come up, based on past experience with Lisa. (I'm probably making her sound like a terrible person, but really she's a very caring, people-focused person, where I tend to be more task-oriented, so I suspect that's where some of the tension comes from. She's thinking "if you cared about me you'd understand that I'm really stressed and would make time to help me," and I'm thinking "I have to get X, Y, and Z done, and they're all both more important and more urgent than what she's asking me to do. Plus X, Y, and Z are my assigned duties, and should be a higher priority for me.")
So, all that said (and thanks for reading this far if you have!), what are some ways I could address this if it happens in another meeting, without making things (more) uncomfortable for the rest of the group? In the previous two incidents, I've basically said something like "sorry, I can't." But what I really want is for the behavior to stop. I'm hoping that Supervisor will address it very soon, but I'd like to have a polite but firm answer ready if Lisa does try it again, and I'm hoping that the wise EHellions can assist.