It is the easiest, to view the context. People tend to postpone unpleasant tasks, therefore may need frequent reminders. Example:

> Wie oft muss ich dir noch sagen, dass du dein Zimmer aufräumen sollst? (How often do I have to repeat, that you shall clean up yoour room?)

So the *task* must be quite a pleasant one, if  no reminder is necessary at all. A typical use is:

> Nimm doch das letzte Stück Kuchen!

So the response

> Dass lasse ich mir nicht zweimal sagen!

indicates something like *it is a pleasure to comply*, typically even exceeding that, i. e. that you wanted to eat the cake anyway, but were too shy to ask for it. So I agree with Devon, that your example is not the typical one, which is a response to a request.