How can I add a due date to OS X Reminders?
You can use AppleScript with this one-liner to create an item with the Due Date independent of the Remind Me Date:

tell application "Reminders" to show (make new reminder with properties {name:"New reminder", due date:(current date)})


Or you can use Automator to create a Service that does the same thing. That way, you can assign a keyboard shortcut to it in System Preferences. See the Services list under System Preferences… Keyboard… Shortcuts… Services.

In Automator, add the New Reminders Item snippet and make sure Due Date is checked. Use menu item File… Save to save the workflow in the default location (~/Library/Services/). The Service should now be visible in the Reminders application, under menu item Reminders… Services….