Coming from prehistoric German, "Till" passed into old English as meaning a goal or fixed point in either space or time. It is said by various websites to have been combined by contraction since the 13th century with the Norse word "und" (pronounced unt) which is said to come from the proto-Germanic word "wundō" which means "wound", but this really makes no sense. It makes much more sense that "till" would have been contracted with the Germanic word "und" (also pronounced unt) meaning "and". More or less, the two together would literally translate to "and to such point".
Therefore the statement "You have until March 1st to pay your rent of $100 to avoid eviction." would translate roughly to "At this present time have you a debt of $100. You may make payment at present and to such point as the date of March 1st to avoid eviction." The latter being quite tedious to say or write, has evolved.
In your example, "you must deliver your product within two days (and to be clear, you have from now and to such point as August 18, 2011) to meet your deadline and get paid." Technically, I suppose, it means you have to deliver the product by 23:59 on 17 August 2011, although a real deadline to a particular point in time should include the actual time. As no time was supplied, it might be compromised to be high noon August 18, 2011. I guarentee you though, it definitely means before the end of the business day August 18, 2011, whatever hour that may be, and more than likely does not mean until midnight the following day unless they have 24 hour receiving.