The concept of Natural Law was an important part of enlightenment legal thinking. When the Declaration of Independence invokes the 'Laws of Nature', it's authors would certainly have been aware of and intentionally referencing contemporary thinking on the subject to justify the declaration.
In fact we know from some legal decisions of the time that Natural Law was explicitly used as justification for various legal decisions, in the absence of explicit written laws on the subject.
As homo sapiens sapiens is a social animal, it's difficult to make the distinction between what it "natural aspirations" and "social consensus".