The problem I see is this:

There is no event name here.  Where are you expecting this to execute?  I
would suspect it should be in the combo's After Update event.

Also, this is a good place to use a Select Case statememt:

   With Me
       Select Case .cboClassification
           Case "UNCLASS"
               .Con_Num_Class = "U"
           Case "CONFIDENTIAL"
               .Con_Num_Class = "C"
           Case "SECRET"
               .Con_Num_Class = "S"
       End Select
   End With
   End If
End If

What event are you using? Should be the cboClassification's After Update
event. Also be sure in your code to preface cboClassification with Me:

If Me.cboClassification = "UNCLASS" Then
   Me!Con_Num_Class = "U"
Else
   If Me.cboClassification = "CONFIDENTIAL" Then
       Me!Con_Num_Class = "C"
   Else
       If Me.cboClassification = "SECRET" Then
           Me!Con_Num_Class = "S"
       End If
   End If
End If

Give that a try. Also might want to use a SELECT Case statement instead.

What does "not working" mean? Are you getting an error message? If so, what
is it? Or is it a case that nothing's going into the text box?

Are you certain that cboClassification returns what you think it does? Try
the following:

Private Sub cboClassification_()
 Select Case Me!cboClassification
   Case "UNCLASS"
     Me!Con_Num_Class = "U"
   Case "CONFIDENTIAL"
     Me!Con_Num_Class = "C"
   Case "SECRET"
     Me!Con_Num_Class = "S"
   Case Else
     MsgBox "The combo box is returning " & _
       Me!cboClassification
 End Select
End Sub

Dave,
  Try...

  You could also use a Select Case Statement to accomplish the same thing.

   BUT... all this is redundant.  If cboClassification is bound to some
field in your table, (say Classification) that would be all you need to
capture.  Having another control to capture the "U" in Unclass, or "C" in
Classified... etc, is redundant.
   Given that you capture "UnClass, you could always calculate and display
the "U" (on the fly) by using an unbound text control with a Control Source
of ...
       = Left(cboClassification, 1)