"it cannot be denied that our government was founded upon a belief that human rights come from God, not governments"

James Conley at First Things has a superb essay on America's Atheocracy:

G. K. Chesterton said famously that America is “a nation with the soul of a church.” And he believed the Declaration of Independence formed the substance of our national soul. 

... [W]e need to recognize that some of the deepest problems in our public life can be traced to our collective neglect of America’s great founding document.

The Declaration establishes our common self-identity as Americans. It tells us that we are one nation under God, a people who believe that all men and women have God-given rights. It tells us that government exists for no other purpose than to defend and promote these rights. All this we find in the Declaration’s preamble, which still has the power to stir us.

Conley notes:

America’s founders never intended to establish a religious government, let alone a theocracy. In fact, just the opposite. They specifically disallowed any state-sanctioned religion. Yet the government they did establish was founded on theistic, if not explicitly Christian, principles.

Many observers have identified a deep Christian influence in America’s founding documents—including such luminaries as Chesterton, Dietrich Bonhoeffer, Jacques Maritain, John Courtney Murray, Martin Luther King Jr., and Blessed John Paul II. 

Others see more the hand of the Enlightenment’s philosophical Deism at work. 

Whatever its precise Christian pedigree, it cannot be denied that our government was founded upon a belief that human rights come from God, not governments, and that the world is in the hands of what the Declaration called “Nature’s God” and “the Supreme Judge of the World.”

It is in this sense that I make this assertion: atheism is inherently inconsistent with human rights and with American democracy.

I am not asserting that individual atheists are opposed to human rights, or are un-American. I used to be an atheist, and I respected human rights and loved America. I served my country willingly (I'm an Army veteran).  But the fact is that I did not understand the logical implications of my atheism.

Atheism itself provides no basis for objective human rights (or for any objective moral law at all), and godlessness precludes affirmation of rights endowed by our Creator. Most atheists are decent people who support rights and love their country. But I believe that atheists are co-opting Christian values.

Conley:

It is true: the Constitution that America’s founders would later draft makes no mention of God. It is also true that this Constitution denies full rights to slaves and women. 

But the Declaration’s belief in the divine origin of the human person is everywhere presumed. And throughout American history, this belief has served as a goad to the conscience, inspiring reforms and renewal in almost every generation. It has ensured that injustice, cowardice, and political expediency do not have to have the final word in our public affairs.

The Christian foundation of our Constitutional system of government has continuously served as a basis for extending rights to all of our citizens:

The Constitution and Declaration together form the “great wells of democracy” that express “the most sacred values in our Judaeo-Christian heritage,” King wrote in hisLetter from the Birmingham Jail. 

America’s founders also shared a belief that religion mattered—not only for the private welfare of individuals but also for the commonweal. 

Conley laments the modern atheist assault on our liberties:

America today is becoming what I call an atheocracy—a society that is actively hostile to religious faith and religious believers. 

An atheocracy is a dangerous place, both morally and spiritually. Cut off from the religious moorings expressed in the Declaration, we risk becoming a nation without a soul, a people with no common purpose apart from material pursuits. 

Conley quotes Chesterton:

The Declaration of Independence dogmatically bases all rights on the fact that God created all men equal. . . . There is no basis for democracy except in a dogma about the divine origin of man. . . . Every other basis is a sort of sentimental confusion … always vain for the vital purpose of constraining the tyrant.

This is precisely the issue. Without belief in God and in an objective moral law, there is no basis for belief in objective human rights. Atheism inherently means that rights are subjective opinions, liable to extinction based on the will of the powerful. Atheist moral law is the law of those strong enough to impose their will. This may seem harsh, and I know it will elicit howls of protest from easily-offended atheists. But I insist: if God does not exist and there is no moral law independent of man's subjective opinions, to what can we appeal except opinion? Why is my view that slavery is wrong any more right than another man's view that it is right, if there is no objective moral law to which we can appeal?

And how can there be an objective moral law if there is no God?