Live notifications in a ToDo list app?

So I am trying to build a somewhat enhanced version of the to-do list app. What I want to achieve is to get a list of the pending tasks from users and store them locally inside the browser localStorage or any other alternative options. Then the user can close the web app if they want. Whenever the task deadline is near, the users will get a notification informing them about the concerned task.

The main part is the functionality of receiving the notifications even when the app is closed(browser is still open though). If the app were open or in an idle state in the background, it could have been simply done using the notifications API but it seems to be more difficult when the app is closed. http://ift.tt/1JanhIg Please guide. Thanks for reading. Any help is appreciated!!