Jon,
Yes, this is quite simple to do using some of our apps available at the Marketplace. Simply go to http://www.clarizen.com/appsmarketplace.html and search for Notification. You will find Notification Manager where there are a number of workflow rules that may benefit you, including sending an email update to a Manager or Resource when a task is assigned, coming close to due date and much more.
Sincerely,
Boris