For sure, I absolutely agree that the US are influenced by Rome and consequently by Greece, I think that is obvious in engineering, architecture or laws...but to assume for that that US is "a new Rome" is a strong affirmation.
So, here's what I want to mean, why the fact that US is influenced by Rome gives you the idea that US is "a new" Rome, if we follow this rule, France, Germany or any european country can be Roma...roman-style buildings are in everywhere, not only in washington and about culture and politics, as it was pointed out before, US culture is similar to the European one (something that I totally disagree too ) so we go again with the same, any country of here can be "a new " rome from your point of view
P.D: Sorry for my English