When creating an assignment from the assignments page in Canvas, it is automatically added to the Calendar on the date you enter. If you don't set a date on the assignment you can still see it on the calendar view by clicking on the "undated events" link on the right pane of the Calendar. You can then drag it on to the calendar.
If you are not seeing the assignments from your course on the calendar make sure the course calendar is checked "on" in the right pane. Moving an item around on the calendar automatically updates the dates on the assignment tab and vice versa.

Items show on the calendar on their due date. Let me know if I misunderstood your suggestion.