The structure of the US government is modeled directly on the Roman Republic not indirectly through the Parliamentary system. It's why we have neither king nor prime minster but we do have proconsul with veto power.
The US common law system is taken directly from English common law which is in turn taken from Danelaw (Norse) and Saxon common law.
I suggest this combination of sources gave the new country the benefits of hybrid vigor which lasted at least a century.
The British Empire was much more accessible to the Founding Fathers. Perhaps they may have claimed a relational system to Rome, but it was within the context of what they knew as the British system. The House of Commons and House of Lords closely resemble the House of Reps. and Senate. The glaring difference is the lack of Prime Minister/King. But keep in mind, England was a constitutional monarchy, the sovereign being both ruler and and subject to the law. The powers of executive are vested within the presidency in the United States. All this is to say the America system, at least in practice, if not ideology, bears a closer resemblance to the English parliamentary system than the Roman Republic. This isn't to claim that differences in each iteration do not exist, only that the early Americans were much more familiar with the British governmental system, and drew more on that experience and theory than the histories recorded by Cicero, et al.
All this is to further say that if any parallels exist between American history and and Jewish history, they are coincidental and are not formally influential on each other.
As a general rule, histories of individual locales and governments may share some parallels, but this is only because they deal in the same administrative realm.
I will end this comment by stating simply that it is my belief that a federal government should take precedence in matters of national importance. To put it another way, if I were alive in the early republic, I would have been in adamant agreement with Alexander Hamilton and James Madison. They constitute, in my opinion, the two greatest political scientists of the early American period (1776-1800).