|The term is "circular reference", not "circulating reference".|
However, what you are asking for is not really a circular reference.
Bear with me for a second...
A circular reference can be defined as follows:
"Circular references occur when a formula refers--either directly or indirectly--to the cell in which the formula is stored."
In your case, you might start with a circular reference:
Sheet1!A1 contains =Sheet2!A1
Sheet2!A1 contains =Sheet1!A1
but as soon as you enter a date in ether of those cells, you remove the circular reference since only one cell will contain a formula.
It's a subtle difference, I'll agree, but since a cell can't contain both "text" and a formula, the instant you try to use your configuration, the circular reference goes away.
However, all that blabber doesn't help you accomplish your goal, does it? <g>
Unfortunately, I don't think you'll be able to do what you want without some VBA code. There are no Excel functions that allow two cells to reflect the contents of each other and allow you to change the contents of either of those cells whenever you want.
Something as simple as a Selection_Change macro with an InputBox would do the trick. Put this in the VBA editor for both Sheet1 and Sheet2 and it'll fire whenever you select A1 in either sheet.
Private Sub Worksheet_SelectionChange(ByVal Target As Range)
If Target.Address = "$A$1" Then
myDate = Application.InputBox("Enter A Date", "Date Entry")
Sheets(1).Range("A1") = myDate
Sheets(2).Range("A1") = myDate