If an amount of money is DUE, it MUST be paid at a particular time:
'The next income tax payment is due on 31 January'
If you fail to pay a bill, for example, by the time expected (in your example, membership fees are to be paid on January 1st) then your bill is OVERDUE. (You can use OVERDUE as an adjective: an overdue gas bill)
Hope this helps.
Student or Learner