In the web app, it does not seem possible to add due dates with smart add.

While there is a help topic (http://help.doit.im/topics/3006) saying that it's possible in the phone apps using the format "due YYYY-MM-DD", the web app will just append the "due…" text to the task description.

Also, if smart add does offer this functionality, it should be documented in the same way as the other options, which is not currently the case.