I don't have a T2, but if the T2 is anything like the Droid Maxx or Turbo: Are you using the stock launcher that came with the phone, or did you install a third party launcher (like Google Now, Nova, Action Launcher)? Only the stock launcher shows the actual date on the calendar icon.
If it's not that, did you install the Google Calendar app? It works almost exactly the same, but the Google Calendar app icon will not update when it is on a home screen.
If not that, did you disable any apps? In particular, did you disable the app "badger"? That's the app that puts the proper date on the Calendar app icon.