Many conservative Christians insist that America was founded as a Christian Nation, despite the absence of any evidence that would support this. In contrast, there is some evidence for the idea that America was founded as a "scientific" nation. What I mean is that principles of science and scientific investigation, as they were understood at the time, were an important influence behind the creation of American democracy and government.
The writings of Newton, Francis Bacon, John Locke and David Hume deeply influenced Jefferson as he drafted the Declaration of Independence. Newton teased out the difference between belief and knowledge. Bacon laid out how we could build knowledge using inductive reasoning. Locke defined how knowledge is different from and superior to "but faith or opinion". Hume defined freedom as the ability to choose to do something or not.
Jefferson incorporated these ideas in America's founding document and they laid the philosophical and legal foundations of the US. If every human had the potential to build knowledge about reality and truth using science, no king or pope could claim a greater authority than an ordinary citizen. All men were created equal. This justified a secular government that respected and tolerated religion, but did not base its authority on religion--instead basing it on liberty, reason and science.
Source: New Scientist, October 29, 2011
It's appropriate that Thomas Jefferson was influenced by scientific knowledge when he also believed that democracy works best when the voting public is well-informed. It all comes down to knowledge about the world around us and the ability to use that knowledge to make our lives better. That's an important part of what defines both science and democracy.
This should be contrasted with our current government where elected politicians are mostly lawyers. Being a lawyer isn't inherently bad, but one of the things which defines a law education is learning how to use facts in a highly selective way to win a case. That's contrary to how science works, which means it's contrary to some of the more important ideas behind the founding of our government.
What should really dominate government and government policy: ideology or facts? If it's ideology, then having lawyers in charge is appropriate and denial of science is only to be expected. If it's facts, though, then we're on the wrong course and need to make some significant changes in order to get back on the right course.