Let's begin with some definitions. Eschatology is the branch of theology that relates to end time prophecies and events. Chutzpah is a Hebrew word that can be translated as nerve, gall, or audacity. When an English-speaking person uses the word, chutzpah, he normally does so to emphasize that a particular statement or action is especially outrageous. So, "Eschatological Chutzpah" refers to a statement about end time prophecy that is characterized by unmitigated audacity.
To understand and appreciate two such statements I have in mind, one further definition is required — the definition of Dispensationalism. This term, as it applies to end time prophecy, refers to those who are Premillennial in viewpoint and who believe in a Pre-Tribulation Rapture. They also believe that the Jews are still the Chosen People of God and that one day, at the end of the Tribulation, a great remnant of them will accept Yeshua (Jesus) as their Messiah. More