Hi Aggie,
I guess I will take a shot at your question...
The New Hermeneutic stems mainly from the Neo-Orthodox movement through Barth and Bultmann. The basic premise is a shifting of focus from the text to the reader. In other words, it gets away from the Western methods of historical-grammatical interpretation in order to focus on the reading-event of revelation from God to the reader.
This is directly related to post-modernism and the reader-response method of interpretation. It is mainly criticized for the obvious neglect of the biblical context and meaning because it is simply relying on a subjective experience and how God uses the bible as a bridge for revelation in the present. Clearly, one will rarely come away with the original meaning in such a subjective hermeneutic.
The New Hermeneutic has taken a beating, but it is not all bad. The Neo-Orthodox movement was kind of a reaction to the modern scholars who hardly moved beyond their contextual studies into a relational aspect of scripture. So you can see how the New Hermeneutic was an attempt to restore what had been ignored for so long: The aspect of God communicating relationally to people through scripture.
The NH is not all bad for this reason. God does reveal Himself through scripture. But the NH falls short because it commits the same crime as the Modern scholars did in leaving out one of the elements of interpretation. The NH neglects context and jumps directly to application (if there is such a thing as application without knowing the original meaning).
If you would like a good overview of Hermeneutics, as well as a discussion of the issues (NH, interpretation vs. application, etc.), a good online read is:
http://www.tms.edu/tmsj/tmsj8e.pdf
Hope this helps!
ischus