Depends on where the cliche is.
If it's a textual cliche--the fire was hot as hell, he avoided her like the plague, that sort of thing--I think that a cliche that makes the story work is much nicer than forced originality that slows the story down and makes the reader think (at the wrong moment). Obviously, if your story is nothing but cliches, there's a problem, but that's rarely the case.
There's nothing wrong with textual cliches--after all, their very potency is what made them used so often that they became cliches--but they lack power. You probably don't want to use them where you need to create an effect, but they can efficiently convey an idea on the way to your payoff.
If it's a situational or plot cliche--we were all living in a jar of Tang! the stranded couple turned out to be named Adam and Eve! The vampire managed to corner the pretty young woman only to discover she was a vampire hunter!--well, that's a more difficult situation. Your story might not survive. In that case, you probably have to dig deeply into the situation and figure out how you can twist it. The jar of Tang you might be able to rescue by starting after the escape, rather than having the realization of the truth be the subject of the story. Alfred Bester thought about the stranded couple and realized that you only needed gut bacteria to seed the earth--same basic idea, but it avoids the Adam and Eve cliche. Maybe the vampire hunter is part of a tag-and-release study of vampires.
In all of those cases, the original story does not survive unscathed.