She's a manager where I work...but not MY manager...?

In the past week she has given me at least half a dozen projects to do on very short notice. Normally, I wouldn't mind helping her out--but it's crunch time at work and my supervisor has given me other projects that need doing.

I can't just tell her she needs to manage her time a little better--even though I really think that is the case--because, even though I don't report directly to her, she is one of the higher-ups.

It's gotten to the point where the very sound of her voice anywhere near my office is like nails on a chalkboard! My usual, tactful ways of fending off requests I don't have time for doesn't seem to be working. Advice please?

If you are comfortable telling this person to please check with your boss and say something like "if she says it's okay then I'm glad to do it for you but I'm really busy with her work at the moment."

If that's not comfortable then take the work she wants you to do to your boss and ask her what priority should the other person's task be given. You can tell your boss that usually it's not a problem to help her but given that you're very busy right now you want to be sure. It's really unfair of her to assign you work when you don't report to her but the bosses should be aware that this is happening and sort it themselves. It's an awkward position she's put you in. Good luck!

talk to your manager and explain the problem to her. she should resolve it with the other manager.

You could tell her you have high-priority projects from your Manager and don't have time to do hers. Or you could tell her you'll have to check with your Manager about scheduling these extra projects into your workload.
You should make your Manager aware of the situation so that you cover yourself for any future problems with this.

Go to your manager with the problem. Make sure you're clear that you don't mind helping her out but that her projects are making it difficult to complete your own work. Hopefully your manager can tactfully communicate to her that you're being bogged down by peripheral projects.

You have to let your supervisor know that you are working on too many projects at once. Maybe he/she can you help you prioritize the projects.

Yep...talk to your manager about it. Tell your manager that you are having a harder time meeting your immediate expectations due to overwork from her.

you tell her that your supervisor has you very busy and you can't do it and have a confrence with your supervisor and let him/her know what is going on