I think the answer to that question is that it depends on who you ask. There is absolutely a group of fans out there who want Michigan to lose every game that they play, there's another that wants them to lose the big and meaningful games, and then there's those that want them to win every game except the Ohio State game. There's a bunch of variation on this topic, some feel much more strongly about it than others.
Cohen's article goes into good perspective on that of other rivalries, like the Iron Bowl between Alabama and Auburn, as well as the Bedlam game between Oklahoma and Oklahoma State.