Well i don't think its necessarily a spoiler because in many interviews Chris Nolan and others have said that he needs to die, Batman needs to be dead at the end because this is the last movie of the trilogy.. He said it would be unrealistic if he was to live. But the fact that David Letterman said HE WON'T BE DEAD is a possible spoiler..
Its not so much if he will die now, but HOW he will die.