This code placed in a Module is working but must say that the entire macro is not efficient. It will loop needlessly 70 times from 20130601 to 20130531 and at every other change of month.
Option Explicit
Sub test1()
Dim strSheets As String '<== added
strSheets = "20130603"
On Error GoTo SkipTab '<== added
Do Until strSheets = "20130528"
Sheets(strSheets).Select
Range("E28:O28").Select
Selection.Copy
Sheets("Sheet1").Select
Range("B3").Select
Selection.PasteSpecial Paste:=xlPasteValues, Operation:=xlNone, SkipBlanks _
:=False, Transpose:=False
Range("A3").Select
Selection = strSheets
Rows("3:3").Select
Selection.Insert Shift:=xlDown, CopyOrigin:=xlFormatFromLeftOrAbove
Range("B3").Select
Sheets(strSheets).Select
Range("E15:O15").Select
Selection.Copy
Sheets("Sheet1").Select
Selection.PasteSpecial Paste:=xlPasteValues, Operation:=xlNone, SkipBlanks _
:=False, Transpose:=False
Range("A3").Select
Selection = strSheets
Rows("3:3").Select
Selection.Insert Shift:=xlDown, CopyOrigin:=xlFormatFromLeftOrAbove
strSheets = strSheets - 1
Loop
Exit Sub '<== added
SkipTab: '<== added
strSheets = strSheets - 1 '<== added
Resume '<== added
End Sub