Speaking as a librarian who hires people, I can tell you that for me, the more notice the better. If you were my employee, I'd appreciate as early a heads-up as possible, because it would give me a chance to plan for a new hire before the school year begins. I'd also want to hang onto a current employee as long as I could, rather than give a resigning person the boot immediately. In the current budget climate, I would be especially loath to give someone the boot immediately. I'd be very surprised if anyone in the UW-Madison libraries did that; but I don't know (and it's not really my business) whether you're on campus or not. In Madison there is always a lot of competition for library jobs, but when hiring is at a near-standstill for budget reasons, I'd question that an employer could replace you that readily. Even more important for me is kind of a corollary: the less notice you give, the worse you look. Every person I hire gets an orientation where (among many other things) they're told to give a minimum of two weeks' notice if they get another job. A grad student I employed this past academic year gave me 3 days' notice, stating that I hadn't notified her in writing of my two week preference. Needless to say, she did not leave a good impression upon departing. So definitely don't be that person.