“Human-like” AI is commonly referred to as AGI, or “Artificial General Intelligence” . I believe that “sentiment analysis” is in fact more closely related to conversational agent (aka chatbot) NLP or AI than people seem to realize.
Keep in mind, there are two layers to “human-like” AI. One is the speech layer, or dialog system (using essentially the same technology as sentiment analysis, but in a different way). The second layer is the “cognitive”, perhaps more like IBM Watson in that it’s actually “understanding” concepts and their relations. So, the fusion of Apple Siri and IBM Watson would give some idea of a more “human-like” AI. Once Apple releases a Siri SDK, and IBM releases its Watson API, then people may begin to hack around and realize this potential. (Of course, the availability of robust AI middleware platforms would also be helpful.)
However, Seth Grimes is probably right that the “easiest” way forward would be with machine learning based on crowd-sourcing. Perhaps one day soon machines will be digesting and learning from Quora.