For each trigger in a template you can specify a due date for new checklists.
If you do not specify this in a trigger, the trigger will look at the template if due date has been set and use that due date for new checklists.
To specify the due date in a trigger open the trigger page by first open the template page and click Set triggers in the action menu.
Select the trigger in the list you want to configure.
Scroll down to the How section on the trigger page, and click on Set due date.
This will show you the set due date page where you specify after how many days from the start of the checklist it is over due.