Regarding the quote from Adams, I'll again refer you to a story told by Thomas Jeferson.
During debate over the wording of the Declaration of Independence, a motion was made to add the words "Our Lord Jesus Christ" after the word "Creator". It was defeated.
There is no doubt America offers (well, it used to) an ideal environment for the practice of Christianity. That is well and good.
But it was not ever a Christian theocracy. Why is that a problem?
"Such being the impressions under which I have, in obedience to the public summons, repaired to the present station, it would be peculiarly improper to omit in this first official act, my fervent supplications to that Almighty Being, who rules over the universe, who presides in the council of nations, and whose providential aids can supply every human defect, that His benediction may consecrate to the liberties and happiness of the people of the United States.." "...Every step by which they have advanced to the character of an independent nation, seems to have been distinguished by some token of providential agency" From President George Washington's Inaugural Address, April 30th, 1789, addressed to both Houses of Congress.
"It is impossible to rightly govern the world without God and the Bible" President George Washington, September 17th, 1796
"Of all the dispositions and habits which lead to political prosperity, religion and morality are indispensable supports . . . And let us indulge with caution the supposition that morality can be maintained without religion . . . Reason and experience both forbid us to expect that national morality can prevail to the exclusion of religious principle." President George Washington
"...The Smiles of Heaven can never be expected On a Nation that disregards the eternal rules of Order and Right, which Heaven Itself Ordained." President George Washington
"I have lived, sir, a long time, and the longer I live, the more convincing proofs I see of this truth -- God Governs in the Affairs of Men, And if a Sparrow cannot fall to the ground without His notice, Is it possible that an empire can rise without His aid?" Benjamin Franklin
"Except the Lord build the house, They labor in vain who build it." "I firmly believe this." Benjamin Franklin, 1787, Constitutional Convention
"The religion which has introduced civil liberty is the religion of Christ and His Apostles.... This is genuine Christianity and to this we owe our free constitutions of government."Noah Webster
"Whether this [new government] will prove a blessing or a curse will depend upon the use our people make of the blessings which a gracious God hath bestowed on us. If they are wise, they will be great and happy. If they are of a contrary character, they will be miserable. Righteousness alone can exalt them as a nation [Proverbs 14:34]. Reader! Whoever thou art, remember this, and in thy sphere practice virtue thyself and encourage it in others." Patrick Henry
"The Bible is worth all other books which have ever been printed." Patrick Henry
"Can the liberties of a nation be thought secure when we have removed their only firm basis, a conviction in the minds of the people that these liberties are the gift of God? That they are not to be violated but with His wrath? I tremble for my country when I reflect that God is just; that His justice cannot sleep forever." President Thomas Jefferson
"The reason that Christianity is the best friend of Government is because Christianity is the only religion that changes the heart." President Thomas Jefferson
"Of all systems of morality, ancient or modern, which have come under my observation, none appear to be so pure as that of Jesus." Thomas Jefferson, To William Canby, 1813
"We have no government armed in power capable of contending in human passions ubridled by morality and religion. Our constitution was made only for a moral and religious people. It is wholly inadequate for the government of any other." John Adams, address to the militia of Massachusetts, 1798.
"I hold the precepts of Jesus as delivered by Himself, to be the most pure, benevolent and sublime which have ever been preached to man..." President Thomas Jefferson
"The highest story of the American Revolution is this: it connected in one indissoluble bond the principles of civil government with the principles of Christianity." President John Adams
"Before any man can be considered as a member of civil society, he must be considered as a subject of the Governor of the Universe. And to the same Divine Author of every good and perfect gift [James 1:17] we are indebted for all those privileges and advantages, religious as well as civil, which are so richly enjoyed in this favored land." James Madison
"We've staked the whole future of American civilization not on the power of government, far from it. We have staked the future of all our political institutions upon the capacity of each and all of us . . . to Govern ourselves according to the commandments of God. The future and success of America is not in this Constitution, but in the laws of God upon which this Constitution is founded." President James Madison
"Providence has given to our people the choice of their rulers. And it is the duty as well as the privilege and interest, of a Christian nation to select and prefer Christians for their rulers." First Chief Justice of Supreme Court John Jay
"Human law must rest its authority ultimately upon the authority of that law which is divine....Far from being rivals or enemies, religion and law are twin sisters, friends, and mutual assistants. Indeed, these two sciences run into each other." James Wilson, a signer of the Constitution and an original Justice on the U.S. Supreme Court
"Let the children...be carefully instructed in the principles and obligations of the Christian religion. This is the most essential part of education. The great enemy of the salvation of man, in my opinion, never invented a more effectual means of extirpating [removing] Christianity from the world than by persuading mankind that it was improper to read the Bible at schools." Benjamin Rush
"It is no slight testimonial, both to the merit and worth of Christianity, that in all ages since its promulgation the great mass of those who have risen to eminence by their profound wisdom and integrity have recognized and reverenced Jesus of Nazareth as the Son of the living God." President John Quincy Adams
"The general principles on which the fathers achieved independence were.... the general principles of Christianity." President John Quincy Adams
"a true American Patriot must be a religious man...He who neglects his duty to his maker, may well be expected to be deficient and insincere in his duty towards the public" First Lady Abigail Adams
"The Bible is the Rock on which this Republic rests." President Andrew Jackson
If there is anything in my thoughts or style to commend, the credit is due to my parents for instilling in me an early love of the Scriptures. If we abide by the principles taught in the Bible, our country will go on prospering and to prosper; but if we and our posterity neglect its instructions and authority, no man can tell how sudden a catastrophe may overwhelm us and bury all our glory in profound obscurity." Daniel Webster
"It is extremely important to our nation , in a political as well as religious view , that all possible authority and influence should be given to the scriptures , for these furnish the best principles of civil liberty , and the most effectual support of republican government. The principles of all genuine liberty , and of wise laws and administrations are to be drawn from the Bible and sustained by it's authority.The man therefore who weakens or destroys the divine authority of that book may be accessory to all the public disorders which society is doomed to suffer...." Noah Webster
"The Bible must be considered as the great source of all the truth by which men are to be guided in government as well as in all social transactions...." Noah Webster
"The moral principles and precepts contained in the Scriptures ought to form the basis of all our civil constitutions and laws...." Noah Webster
"All the miseries and evils which men suffer from vice , crime , ambition , injustice , oppression , slavery , and war , proceed from their despising or neglecting the precepts contained in the Bible...." Noah Webster
"The religion which has introduced civil liberty is the religion of Christ and his apostles , which enjoins humility , piety and benevolence ; which acknowledges in every person a brother , or a sister , and a citizen with equal rights. This is genuine Christianity , and to this we owe our free constitutions of government...." Noah Webster
"It is the sincere desire of the writer (Noah Webster) that our citizens should early understand that the genuine source of correct republican principles is the Bible , particularly the New Testament or the Christian religion." Noah Webster
"I believe the Bible is the best gift God has ever given to man. All the good from the Savior (Jesus) of the world is communicated to us through this book. Abraham Lincoln
"Our laws and institutions must necessarily be based upon and embody the teaching of the Redeemer of mankind. It is impossible that is should be otherwise; and in this sense and to this extent our civilization and our institutions are emphatically Christian . . . this is a Christian nation." US Supreme Court, 1892
"The fundamental basis of this nation's law was given to Moses on the Mount. The fundamental basis of our Bill of Rights comes from the teaching we get from Exodus and St. Matthew, from Isaiah and St. Paul. I don't think we emphasize that enough these days. If we don't have the proper fundamental moral background, we will finally end up with a totalitarian government which does not believe in the right for anybody except the state." President Harry S. Truman.
"History fails to record a single precedent in which nations subject to moral decay have not passed into political and economic decline. There has been either a spiritual awakening to overcome the moral lapse, or a progressive deterioration to ultimate national disaster" General Douglas MacArthur