Real-time monitoring cannot be done in InfoPath alone since InfoPath forms are not persistent (running all the time). You would need a backend process or service that would constantly monitor tasks and dates and generate the notifications. Or like Kalyan says scheduled jobs that would run each day or periodically to check the data.
Maybe you could use a JavaScript/windows script, which I have done before, to run an InfoPath form, pass it some data if neccessary, and have it submit to email. It would need to have full trust and code to comepletely automate without any user intervention. This form would load the task data, check dates, and create a disribution list to email reminders to. This is assuming you are using a database to store the task information so it is easy to load from multiple forms. So this could possibly be a solution. You would need a PC or server to run it at specific times via task scheduler. Low tech could also be to have an office admin or user run the form each morning and with a couple clicks generate the reminder emails.
Typically what I do is just create alert/reminder sections within the form. Hopefully they are acessing their tasks on a regular basis via an existing InfoPath form. Then I use Open rules to check for due tasks and if true either route them to another view with bold/red/highlights/warning notifying them of their due dates and task status or have a hidden section which would appear on the main view doing the same thing. It relies on them accessing the form regularly but is much simpler to pull off.
Some other options, again with a database, is either to have web dashboards which display current tasks and highlight immenent ones or creating a script that checks the data and generates an email that is just a reminder. It depends if you need them to have the form in the email again. Another option would be integrating with Outlook and adding the tasks to their Outlook tasks and relying on Outlook functionality to track the task to completion.
You may be interested in our DBXL application since it databases all of the forms and has built in visibility tools for users to see their forms and would not be dificult to maybe modify the web dashboard for your status tracking. Also the project tracker solution might have some of the functionality you are looking for.
Hope this helps