Thanks guys for the replies in this thread. Some situations which I thought extreme are apparently common occurences in this biz! I feel better.
Of course, we are entertaining, and if we can better please the audience by doing requests, fine. The cheat book of songs you don't include in your set, but will sing if you have to, is a good one, I'll do that I think. I, too, prefer to have a song well rehearsed before I go public, but for requests, usually to please one person who isn't particularly interested in whatever else you're doing, the cheat sheet will do fine.