In my opinion, the use of different tenses depends on the time of reference.
1). My research was due today.
I think this sentence can be used after office hours regardless of whether the research was finished or not.
(a) My research was due today but I need two more days to finish it.
(b) My research was due today, fortunately I had finished it before I left.
2). My research is due today.
I think this sentence is used before the office is closed, also regardless of whether the research is finished or not.
Please correct me if I’ve made any incorrect assumption.