The inventory of historical analogies in contemporary discourse is limited. With only a precious few common reference points, it is inevitable that these references end up being overworked. Above all, World War II is today pressed into service as an analogy for virtually every foreign policy scenario. And not too far behind, surely, is the fall of Rome (a term that people use interchangeably for both the end of Roman Republicanism and for the much later collapse of the Roman Empire).
Rome has great appeal as a model for the West and for America especially. The Romans are considered the prototypical Westerners; for America the Roman Empire represents the archetype of both Republicanism and global domination. The United States was explicitly modeled on the Roman Republic both institutionally and aesthetically. Americans are proud of both their democracy and their enormous power, and Rome stands as a cautionary tale of a state that had both of those things and lost them.
Comment: For a further in-depth analysis of Caesar's role in the birth of Christianity read: From Paul to Mark: PaleoChristianity