SharePoint does not support using today's date in a calculated column and the fields are not recalculated unless a value in the item changes.
Here is a solution you could try using SharePoint Designer and conditional formatting:
- Create another calculated column to hold [Due Date]-3 (e.g. Warning Date)
- Create your [Almost Due] column and put your message as the default value, e.g. URGENT
- Open your Task List in SharePoint Designer and click on the View you want to customize.
- Click on the Almost Due column in the ListViewWebPart and choose Conditional Formatting > Format Column in the ribbon.
- Condition: [Warning Date] > [Current Date]
- Set Style: Font color = White, which should hide the message
Rather than displaying/hiding a message, you could use the conditional formatting to change the color of the Due Date to Red or anything else that you think would alert your user.