It would depend on the context. What about?
EX: When do I have to submit it (by)?
EX: What's the due/submission date?
EX: What day is it due?
EX: What day does it have to be submitted (by)?
EX: What's the last day (that) it has to be sumbitted?
deadline is an old military term. There were two (invisible) lines: the battleline, the one facing the battle, and the deadline, the one facing the other way. If a soldier were to run away from the battle;i.e., run in the opposite direction of the battle, he would automatically be shot (by his fellow soldiers), and hence the term deadline. Academically speaking, if you don't submit your work on time, by the deadline, you're dead.