Your comment made me realize my problem with deadlines. Whenever I hear about a deadline, it has always been the case that management would like to have a time

Your comment made me realize my problem with deadlines. Whenever I hear about a deadline, it has always been the case that management would like to have a time constraint without giving in from any of the other constraints, e.g., scope, budget, quality. It's like trying to find a solution to a set of equations when constraints guarantee that there is none.