Hi Jean first and foremost performers MUST keep the audience happy. That is a given. If it is expected for you to play your own original music then that is what you do. Same applies to covers. If they want covers you give them covers. OK you can put your own style or slant on them. There is enough room for both covers and new music and I like performing both.
Most live bands perform cover stuff until they have a fan base or have as you say hit the bid time. With solo artists it is quite different. Most solo acts play acoustic music generally for listening to as opposed to dancing to.
In my experience as a gigging band or solo cabaret folk on a night out want to dance to music they know. Whereas there are some small acoustic folk music venues and coffee shops where people may want to listen to original music.
I have always played the larger type of venues where a crowd of 200 plus want to boogie as opposed to a handful of people who like to relax and listen to acoustic music and that is what I base my observations on.
Anyways it does not matter, the important point is that a good band or artist/entertainer will be able to please an audience by playing what they want to hear as opposed to what the artist just wants to play. Anything else is doing an audience and yourself no favours.
It should also be pointed out that singer songwriters performing is a whole different ball game to a pro gigging rock band/cabaret act.

http://www.soundclick.com/bands/songInfo.cfm?bandID=687727&songID=5238055