Folks, I have been in this industry for more years than I care to remember, and this has been a problem since there were computers to be fixed. I started on the Help Desk (back when computers were coal powered!), moved to HD Manager, Department Manager, Director, and am currently a PM for Hewlett Packard, working some of their larger corporate accounts. Take it from me: the VIPs come first, have always come first, and will always come first.
We always try to view things in the "perfect world", but in my experience, there is no such thing. A VP is a VP, and will eventually get what he/she wants, whether it is from you or someone else. If you say "no" to him/her, I can guarantee it will be the topic of discussion in the next Executive meeting, with the CIO being blind sided about the issue. One way or the other, the VP's problem will be addressed, and if it comes from the CIO, the priority will be even higher.
Saying "no" to a VP is called a "CLM" (Career Limiting Move).
Complain to your boss, your co-workers, mutter to yourself, or go to the loading dock and scream obsenities into the air, but do yourself and your department a favor and take the call.