Wtong. English common law or the Law of Nations? I vote for the latter as having the most influence.
You may think whatever you like - what is true is that the Bible and Blackstone form the precedence of American Law...
But Blackstone's chief contribution was to create a succinct, readable, and above all handy epitome of the common law tradition. While useful in England, Blackstone's text answered an urgent need in the developing United States and Canada. In the United States, the common law tradition was being spread into frontier areas, but it was not feasible for lawyers and judges to carry around the large libraries that contained the common law precedents. The four volumes of Blackstone put the gist of that tradition in portable form. They were required reading for most lawyers in the Colonies, and for many, they were the only reading. Blackstone's Whiggish but conservative vision of English law as a force to protect people, their liberty, and their property, had a deep impact on the ideologies that were cited in support of the American Revolution, and ultimately, the United States Constitution.
src
Vattel was all the rage in Europe, and undoubtedly under girds the enlightenment there - Europe's liberty being formed on the basis of man and science... American law necessarily allows for the Creator, and assumes protection of the rights given by Him as being the reason for government. Thus 'natural law' has always been Blackstone as observed through the prism of Hebraic law... The grand tradition of Blackstone being the 'natural law' of the Celts going back 1500 years.