Americans do not actually think this. The highway system, environmental protections, labor laws, the military, Medicare, and Social Security are all extremely popular.
What Americans actually believe is that government actions should not be trusted merely because they are government actions.
The fundamental concept of American governance is that the people are sovereign, not the government. This was a radical notion in the 18th century, and I would argue that is remains so today, given the number of folks who can't seem to wrap their heads around it.
For example, gun ownership is not based on the right to rebel--no such right exists (see: the Civil War). Americans have the right to own guns because Americans want to own guns, and Americans are in charge. We get to decide what we want to do and when we want to do it. The role of government is not to rule the people, but to adjudicate peacefully between the many different opinions that people freely hold.
The 2nd Amendment is still in force today not because it is old, but because the American people, today, want it to remain in force.