There are no due dates for discussions. However, students have access to a widget called "Work To Do" and is the equivalent of your "Quick Eval" widget- it shows them any upcoming or overdue course items with a due date. However, Discussions will NOT appear unless you give them an "end date." Go to the "Course Admin" tab in the blue navbar:

 

 

Scroll down and click on "Discussions" in the Communication section

 

 

Then click on the caret next to the discussion you want to edit dates for and then click "Edit Topic"

 

 

Then click on "Available Dates & Conditions" on the right side of the page 

 

 

Finally, enter an "End Date" and click the blue "Save and Close" button.

 

 

Once you have set a date you can click the options under the end date to open the options menu

 

From here you have the option to allow students to view their submissions and replies, but not submit additional responses. 

 

or to restrict their access to the item after the end date all together. 

 

You can also add the availability dates to the students calendar by checking this box.