Not to be argumentative, but the so-called Hebrew Bible is the Old Testament for Christians, and just a part of the Bible which was so influential in early America.
Calvinist theologythe most influential form of Christianity in early America closely integrates Old Testament and New Testament teachingswhich are interdependent on one another. The Old Testament though, is always seen through the lens of the New Testamentwhich is why weve never had laws requiring the death penalty for adultery, or blasphemyamong other sinsas the Old Testament civil law (for ancient Israel) requires.
To separate Old Testament teachings though, from those of the New Testament, does not accurately represent the Christian synthesis of the two, found in early America.
It was the Protestants that were the prime movers behind the ideas that became America.