I personally think that having weekdays as due dates is quite frustrating as it requires additional cognitive load to know today is what day in week (e.g. Saturday) and look at the task due day (e.g. Thursday) then make a subtraction (or a count) to comprehend the urgency of the task.
I argue that by looking at a full date, it is easier for people to know the urgency of a task based on its deadline by simply subtracting the task due date (e.g. 19 March) with today’s date (e.g. 14 March). The answer for the example is obviously “rougly 5 days”.
In conclusion, I prefer having specific dates (example: 14 March instead of Saturday).
P/s: Please leave Yesterday, Today, and Tomorrow as task due date because I think these tags are extremely intuitive and helpful. Great invention! Thank you.