In one long paragraph Carroll provides us with an appropriate understanding of how broad the words of the Declaration really are:  

Ironically, even as revolutionary cohesion was thus excluding, its assertion was simultaneously made to extend to the whole human race - with all people “endowed by their Creator with certain unalienable rights.” From the start, the American tradition assumed that humans everywhere could be expected to embrace a Jeffersonian notion of freedom. So despite the Founders’ exclusivism about race and other matters, their universalism informed structures of liberal democracy that sponsored an ongoing expansion of the American “we.” Federalism, bicameral government, division of powers, checks and balances, Bill of Rights - all adding up to a system, in effect, of revolutionary openness. Even the excluded could see such possibility. In an 1852 oration entitled “What to a Slave is the Fourth of July?” Frederick Douglass turned the Founders’ “we” against itself by declaring of slavery, “We pronounce [it] to be an abomination in the sight of God.” Douglas’s “we” and the American “we” would eventually become the same thing.

Perhaps that is why so many African-Americans fought on the side of the Union in our Civil War.  Or to return to the time of the words, why so few enslaved African-Americans took up the British offer of manumission were they to aid the British in crushing the Revolution already more than a year old in July of 1776.

Carroll does not talk specifically about American Exceptionalism, but such a discussion is surely appropriate in the context of this day.  The idea is older than the nation:  one can clearly find it in the words of John Winthrop of Massachusetts Bay , who in 1630 preached a Sermon on board the ship Arbella to the newly arriving settlers of Massachusetts Bay Colony, who offered these words:  

for wee must Consider that wee shall be as a Citty upon a Hill, the eies of all people are uppon us; soe that if wee shall deale falsely with our god in this worke wee have undertaken and soe cause him to withdrawe his present help from us, wee shall be made a story and a byword through the world, wee shall open the mouthes of enemies to speake evill of the wayes of god and all professours for Gods sake; wee shall shame the faces of many of gods worthy servants, and cause theire prayers to be turned into Cursses upon us till wee be consumed out of the good land whether wee are going

  Half a century ago John F. Kennedy reaffirmed those words in an address to the Massachusetts General Court given as President-Elect. He noted

...I have been guided by the standard John Winthrop set before his shipmates on the flagship Arbella three hundred and thirty-one years ago, as they, too, faced the task of building a new government on a perilous frontier. "We must always consider", he said, "that we shall be as a city upon a hill—the eyes of all people are upon us". Today the eyes of all people are truly upon us—and our governments, in every branch, at every level, national, state and local, must be as a city upon a hill — constructed and inhabited by men aware of their great trust and their great responsibilities. For we are setting out upon a voyage in 1961 no less hazardous than that undertaken by the Arbella in 1630. We are committing ourselves to tasks of statecraft no less awesome than that of governing the Massachusetts Bay Colony, beset as it was then by terror without and disorder within. History will not judge our endeavors—and a government cannot be selected—merely on the basis of color or creed or even party affiliation. Neither will competence and loyalty and stature, while essential to the utmost, suffice in times such as these. For of those to whom much is given, much is required..

Others have referred to Winthrop's words, and one can well argue that those words underlie Eisenhower's willingness to accept the proposal of the Knights of Columbus to add the words "under God" to the Pledge of Allegiance.

There was something inspiring about our declaring independence from England.  It drew people of many nations to our cause of fighting for the Independence we had claimed, and it is fair to note that we might well have lost the war which earned us our freedom absent the participation of those who came to help us.  You will know some of the names, but perhaps not as many as you should.  If you read this 2008 article by Roger Saunders you will see names familiar -  Lafayette, Von Steuben, Kosciuszko, de Grasse, de Rochambeau - but also others of whom you might not have heard, for example:

Baron Johann de Kalb - Germany
He commanded the Maryland and Delaware Continentals who fought bravely in the battle of Camden. He died on his horse as a Major General at the head of his troops, leading a counterattack on the British lines.

Jose Monino de Redondo Count of Floridabanca - Spain
Floridabanca was the Spanish Minister of State who did more than any other Spanish government official to get Spain to enter the war as America's ally

Caron de Beaumarchais - France
He was responsible for setting up a private trading company that France could use to covertly funnel supplies to the colonies at the beginning of the conflict.
Read again Saunder's description of de Beaumarchais -  long before Franklin was able to use the American victory at Saratoga to persuade France to officially enter the war on the American side, he played an important role in keeping the Continental Army appropriately equipped.

Most of those named by Saunders were of the nobility, but still saw the value of what we were doing, even beyond weakening the power of a traditional enemy.   There were others who came as individuals to fight on behalf of the American ideal proclaimed in the Declaration of Independence.  This is a pattern that has continued throughout our history:  some would continue to come and enlist in the American military in order to earn citizenship - there were a pair of brothers from Central America in my boot camp platoon at Parris Island in 1965.  Today we have undocumented aliens who serve, get injured, and even die in our ongoing military conflicts.

Much of the greatness of this nation has come from immigrants.  I teach in Maryland, a state whose Constitution written after independence denied the right to hold public office to anyone not Christian, continuing a pattern going back to the Act of Toleration which offered same only to those who confirmed belief in the Holy Trinity.  The man most responsible for changing that was Thomas Kennedy, a Protestant who emigrated from Ireland, and who when he began advocating for what became known as the Jew Bill had never even met a Jews.

There are so many others who have contributed greatly.  American industry and philanthropy both are greatly indebted to Andrew Carnegie, born in Scotland.  Carl Schurz was born in Germany, became a union Major General in the Civil War, and was the first German-born American to serve in the US Senate, and originator of the famous words : "My country, right or wrong; if right, to be kept right; and if wrong, to be set right."

Many of our Nobel Laureates were born overseas.  In part we can thank the intolerance of the likes of Hitler for their presence in our country.  They became American as did so many others who fled tyranny and/or discrimination in their own nations.  Consider just a few of those responsible for our dominance in the development of nuclear weapons:  Hungarian-born Edward Teller, German-born Hans Bethe, HUngarina-born Leo Szilard, Italian-born Enrico Fermi . . . .

Despite our lack of perfection as a nation or a society, Jefferson's words struck a chord around the world, as did the idea of America.  Despite our periods of isolationism, chauvinism, smugness about our supposed superiority, etc., the idea of America continues to appeal.  It has been so to those from without our borders, just as it has been so for those inside not yet fully included.  Carroll notes the words of the former slave Frederick Douglass.  We might also note the words of another African American, Langston Hughes, from whose Let America be America I would like to go through about 2/3 of the poem, in sections.

First, of the ideal:

I am the poor white, fooled and pushed apart,
I am the Negro bearing slavery's scars.
I am the red man driven from the land,
I am the immigrant clutching the hope I seek--
And finding only the same old stupid plan
Of dog eat dog, of mighty crush the weak.

I am the young man, full of strength and hope,
Tangled in that ancient endless chain
Of profit, power, gain, of grab the land!
Of grab the gold! Of grab the ways of satisfying need!
Of work the men! Of take the pay!
Of owning everything for one's own greed!

I am the farmer, bondsman to the soil.
I am the worker sold to the machine.
I am the Negro, servant to you all.
I am the people, humble, hungry, mean--
Hungry yet today despite the dream.
Beaten yet today--O, Pioneers!
I am the man who never got ahead,
The poorest worker bartered through the years.

Yet I'm the one who dreamt our basic dream
In the Old World while still a serf of kings,
Who dreamt a dream so strong, so brave, so true,
That even yet its mighty daring sings
In every brick and stone, in every furrow turned
That's made America the land it has become.
O, I'm the man who sailed those early seas
In search of what I meant to be my home--
For I'm the one who left dark Ireland's shore,
And Poland's plain, and England's grassy lea,
And torn from Black Africa's strand I came
To build a "homeland of the free."

And then remarking upon the incompleteness of that dream:  

Who said the free?  Not me?
Surely not me?  The millions on relief today?
The millions shot down when we strike?
The millions who have nothing for our pay?
For all the dreams we've dreamed
And all the songs we've sung
And all the hopes we've held
And all the flags we've hung,
The millions who have nothing for our pay--
Except the dream that's almost dead today.

Rereading that one stanza, I cannot but help consider how appropriate, 235 years after the Declaration, they remain for too many Americans today.

Yet Hughes did not despair.  The rest of the poem is a proclamation of his belief about what America could and should be.  It is worth noting that he saw it not only in terms of the liberty of individuals, but also of the freedom of the very land upon which we live and toil and continue to dream:  

O, let America be America again--
The land that never has been yet--
And yet must be--the land where every man is free.
The land that's mine--the poor man's, Indian's, Negro's, ME--
Who made America,
Whose sweat and blood, whose faith and pain,
Whose hand at the foundry, whose plow in the rain,
Must bring back our mighty dream again.

Sure, call me any ugly name you choose--
The steel of freedom does not stain.
From those who live like leeches on the people's lives,
We must take back our land again,
America!

O, yes,
I say it plain,
America never was America to me,
And yet I swear this oath--
America will be!

Out of the rack and ruin of our gangster death,
The rape and rot of graft, and stealth, and lies,
We, the people, must redeem
The land, the mines, the plants, the rivers.
The mountains and the endless plain--
All, all the stretch of these great green states--
And make America again!

We still have our xenophobes.  As Carroll notes of Maryland where I teach, more than 100,000 signed a petition to overturn the state's version of the Dream Act.  Far too many forget the barriers their ancestors overcame in order first to come to this nation, and then to become fully included therein.

Carroll reminds us of Samuel P. Huntington's 2004 polemic “Who Are We? The Challenge to America’s National Identity"  and describes it as "a warning that the arrival of millions of Hispanics threatens the “core culture” of the United States. "  Huntington was late to this line ar argumentation -  we heard it from the likes of Pat Buchanan in the past two decades, it clearly was reflected in things like the Chinese Exclusion Act and the Gentleman's Agreement which restricted further Japanese immigration to the US.  It is older than that, and can be seen in the Know-Nothing movement of the 19th century.

Yet the words of the Declaration are despite the limitations of the men who wrote and signed it far more inclusive than such xenophobia.  It is why when I inquire I find that fully 1/2 of my students have at least one parent born in another country.  

I began as Carroll began.  I will conclude as he concludes, with his final paragraph:  

But the Fourth of July celebrates a vision of national identity that has proven far more open-armed than those who articulated it knew. Millions of Latinos are already joining the American “we,” whatever legislators do. (“We need to tell everyone that we exist,” a 21-year-old undocumented college student recently declared, launching a sit-down protest.) Huntington was right to see a coming transformation of the core culture, but that’s the point. When a settler nation became an immigrant nation; when a white Protestant nation became a multiethnic nation; when an establishment nation became a democratic nation, the culture was shown to be expansive at its core. When the founders said “we,” they were opening a door, not closing one. So - happy Fourth of July.

Peace.