Nita,
In the Indicators column Microsoft Project will show a Red Diamond with a
white Exclamation mark in it to indicate that the deadline has been missed.
Additionally, the Gantt chart will have a Green outlined arrow on it
indicating the Deadline date.
If you are managing the project then these two indicators should be
sufficient to inform that you are approaching, or have breached, the deadline.
I'm not aware of a facility in Microsoft Project that will automatically
generate you a mail but there may be ways that using VB can help?