I think, the following calculation will help you.
Toady() is equal to Current Date ---- (Today is 25 -Jun-2015 IST)
1) Create a calculation like below.
If datediff( 'day', [Order_Date], today())<=0 and datediff( 'day', [Order_Fullfillment_Date], today())>=0 then [Show required Measure] end
2) Drag the Order ID or Referencing of Order ID Column into Columns Shelf.
3) Drag the Above calculated field, select the marks Type "Line"
Thanks for the suggestions so far. I tried the Today statement, but that didn't work as it only references the current date - not the differing dates that are being plotted in the figure. Kettan's response might work, but is less than ideal from a performance standpoint. Thinking about it some more, an alternative approach would be to have a Date range on the x-axis, then do a count of the number of records where [Order_Date]<Date, and do a count of the number of records where [Fulfillment_Date]<Date. This will give us two lines. If we can then calculate a third line that represents the difference between lines 1 and 2, it should be want is required. Is it possible to reference the value of one line in determining the value of another line?