Consider the prototypical sentence:
Let us get back to me watching TV.
What's the correct breakdown of each piece of this sentence? I was trying to use this as an example of why the correct pluralization of the object should be, e.g.,
Let us get back to John and me watching TV.
Let us get back to John and I watching TV.
I realized that I was not actually sure of the correct way to parse the sentence and I was relying on the logic that "me" should become "John and me" rather than "John and I" but I could not come up with the correct grammatical argument. It seems that the prepositional phrase "back to" takes an object and so the objective form "me" is invoked. What's the explanation for the prepositional phrase requiring an object in this case, though?
Edit: Some comments take issue with my example sentence. Consider instead, then:
Let us returen to discussing me watching TV.