That’s a really huge lie that most fundies accept uncritically because it flatters their sense of self-importance.
The Puritans were a bunch of crackpots that I doubt modern fundamentalists would approve of or get along with. The Founding Fathers were a bunch of Deists (closeted atheists, really) and Thomas Jefferson took a scissors to the New Testament to remove the parts he didn’t like, including any miracles Jesus was supposed to have performed.
The only resonance between the Founders and modern authoritarian Christians is that they were elitists or at least believed the elites should be in control as the most dignified and worthy representatives of the citizenry, and that blacks were, at best, 3/5 of a person and illegal as anything but chattel slaves.
And those things aren’t really what the NT authors at least nominally taught (it is easier for a camel to pass through the eye of a needle than for a rich man to enter the kingdom of heaven; god will judge you for failing to be nice to strangers and foreigners; Jesus hung out with all sorts of “sinners” – prostitutes and tax collectors, properly in the same category, lol. The only person righteous enough to bind up the wounds of a man laying by the roadside was a Samaritan – the equivalent, for that time, of what Trump is making out Somalis to be or what Vance was making out of Haitians during the campaign.