How do you create a view in which users can assign tasks to themselves?
Please go through the following modules,

To do list for Drupal 6 only


  Offers a content-type for a simple To do list. It can be used for anything that needs to be done: getting milk at the store, reminding yourself to update a profile, telling your users to vote on a poll by a certain date...


and myTinyTodo - Available for D6 &amp; D7


  A simple way to manage your todo list. This module is based on myTinyTodo.


Otherwise you can do the same system with your current approach