What's the difference in meaning between a and b?

"Please leave me alone and stop talking, Jim."

a. "I haven't said anything."

b. "I didn't say anything."

With the present perfect, there is a connection to the present. But in this sentence, I'm not sure if there is a difference... Could you say that the present perfect stresses that it affects the present time (that his not saying anything affects Jim now)?

My opinion is that there could well be no difference in intent. I believe that Americans tend to use B more than Brits do. However, A can also strongly suggest that Jim does indeed intend to say something.
Context is everything here.
With the first speech in memory, we assume both replies mean "since we have recently been together."

If the first speech were, "You promised to keep your mouth shut about the caper," both a. and b. could refer to any time between the caper and the very recent past. The caper could have been ten years ago.

Connection to the present be danged.
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Connection to the present be danged.

Edit: I think I misunderstood you. Understand you now Emotion: smile
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