Have Americans completely abandoned their belief in the "natural rights of man" ?

Americans make a huge deal out of their founding documents (the Declaration of Independence and the United States Constitution), but few would acknowledge that those documents, and the United States itself, were founded on "natural rights."

What are "natural rights"?   These are the rights of all human beings; rights we all enjoy simply because we are human beings.  These rights are not granted by governments, or laws, or constitutions and, therefore, they cannot be abolished by governments.

Natural rights are the rights of all people, everywhere ... not granted by virtue of citizenship in any one country or adherence to any of the "one true" religions.

I'm not going to try to sell libertarian principles, but I would say this, libertarian thought is completely grounded, just like the United States itself, in the whole notion of "natural rights."  Libertarianism is completely consistent with every founding principle of the American nation.   The whole basis of libertarian thought is based primarily on the recognition of natural rights.  And if you want to understand American principles, read a modern explanation of libertarian theory.  I'd recommend the first three Chapters of Murray Rothbard's book For a New Liberty: The Libertarian Manifesto, first published in 1973. (download it for free)

If you prefer to avoid modern libertarian ideas completely (and I think that's understandable), you really need to read the works of those Western thinkers of the "enlightenment" whose ideas spawned the American revolution. John Locke (1632–1704) was one of the first and most  prominent of those who conceptualized rights as natural and inalienable. Locke, Thomas Hobbes, even Thomas Paine (Common Sense and Rights of Man), Alexander Hamilton and James Madison (the Federalist Papers).

Thomas Jefferson in the 1776 United States Declaration of Independence, famously condensed this to:

We hold these truths to be self-evident, that all men are created equal, that they 

are endowed by their Creator with certain unalienable Rights ...

Thus, America, perhaps uniquely in the annals of history, was a nation born in an explicitly libertarian revolution, a revolution against global empire; against taxation, corporate favoritism (primarily trade monopoly), and against militarism and concentrated centralized power (in a monarch or chief executive).

But Americans have strayed far from that tradition, and have changed dramatically to become the most powerful enemies of the notion of natural rights on the planet, systematically destroying it everywhere, replacing it with the idea that rights are a gift to other nations by the great and wonderful United States.  No matter if hundreds of thousands of people are dying; at least they're free from communism, or Islamist fundamentalism, or some other "-ism" just as evil.

And the US has a list of other nations that it wants to "gift" with their form of democracy.  I just can't understand why they'd resist, can you?

Most Americans are 1) authoritarians and 2) they are statists.  Both of those things stand in opposition to the concept of natural rights. Most Americans today believe that any rights we enjoy are granted by the laws created by men, protected by the armies of men, and are limited to those people who live under the protection of those states which recognize these rights in their legal systems.

The traditional American notion, long since abandoned, is that we all (every human being by virtue of our humanity) possess certain unalienable rights (we cannot be separated from them).  The men who enshrined this belief in the American Declaration of Independence believed so strongly in natural rights that they considered it a "self-evident" truth; in other words, they believed it was an obvious truth that didn't need further justification.  At that time, if you'll recall, the concept of natural rights certainly wasn't obvious or recognized by those who believed in the so-called "Divine Right of Kings", the monarchists or Tories who believed that defying the will of the King was heresy, the King ruled by divine appointment, not by the "consent of the governed."

Most Americans are authoritarians.  It surprised me when I realized that.  I had been so steeped in the "myth" of the rugged, courageous and independent American, I wasn't able to see how badly the myth differs from reality.  Americans are largely followers.  And while I thought for a long time that the Democratic Party offered an alternative to the "goose-stepping" obedience of the Republicans that surrounded me in the Deep South, that notion was shattered when Democrats gave their unquestioning support and allegiance (especially in the first two years of his 1st term in office) to the war policies of President Obama.  Because he was "their" leader, everything they criticized the former President for was suddenly A-OK.  Authoritarian followers.

Most Americans are statists. Statists believe that a large, powerful, central government is desirable; they may argue endlessly over whether that government should be be primarily a "welfare state" or a "warfare state," but in the end, neither side being willing to compromise on its goals for society, Americans will continue to live with government attempts to have both.  And, in the end, they'll live under a totalitarian state, essentially one that is financially unsustainable, and an enemy to liberty.

In short, Americans believe that government grants them their rights; and government can rescind those rights.  And I don't accept that belief.  Do you?  To the contrary, that implicit trust in government is all that is necessary to ensure those rights will be abridged.