That is what the conditional format has in the example I attached. You don't have to add a column to have conditional format you can write the formula to point to the cell with the date.
Now if you did want to have a column that gives you days you can write a formula in it to tell you the number of days past due, or days till the due date and you can conditional it several different ways.
I attached an updated data range file that shows the different ways you can use conditional formatting.
Just check it out and it won't be long until you will be coming up with different ways to use conditional formatting.
I intentionally referred to different elements to show examples how you can use cell values and formulas, though there are many different ways (some easier) to come up with the same results.
Hope this helps.--
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