I work with very busy and important people, and I have to schedule meetings for them all to attend.
This is pretty much impossible.
(By the way, if you need to do the same, I highly recommend whenisgood.net.)
Anyway, I had to set up a meeting with many busy and important people, and of course there was no time that everyone could meet in the next couple of weeks. After days of back and forth, I finally picked a time that only three people would miss, and sent out an email with that time.
Within 10 minutes, two of the three people who were not available for that time slot sheepishly sent me an email saying that they could, in fact, be there for that meeting.