Wall of Separation Between Church and State...This Phrase Isn't in the Constituion

That phrase isn't in the Constitution of the United States. It is in a statement by Thomas Jefferson in a letter to the Danbury Baptist Church in Connecticut dated January 1, 1802. Jefferson's phrasing was inspired by a locution of Roger Williams who founded the original Baptist church in the U.S.A.

Below is the locution by Roger Williams in 1644.

"[A] hedge or wall of separation between the garden of the church and the wilderness of the world,"

So Jefferson was inspired by a Baptist preacher when he wrote the separation of church and state phrase. Yet, it is quoted by atheists as if it promotes their cause.

See Jefferson's Letter to the Danbury Baptists at link below.
Jefferson's Letter 

The Danbury Baptists were worried about government interference in religious expression and practice and Thomas Jefferson understood this. They thought that "free exercise of religion" being in the Constitution might be construed as the government giving people that right and not as it being inalienable meaning given by God.  

According to David Barton at Wallbuilders.com, Jefferson enunciated several times that the federal government didn't have a right to regulate or impede religious expression. 

One such instance occurred in Jefferson's Second Inaugural Address, 1805. See quote below.

"In matters of religion, I have considered that its free exercise is placed by the Constitution independent of the powers of the general [federal] government."

The above quote can be found in A Compilation of the Messages and Papers of the Presidents, 1789-1897 and in Annals of the Congress of the United States of 1805.

In 1947, the Supreme Court made a decision in the case of Everson v. Board of Education. In their definition of the establishment clause of the First Amendment, they put this at the end: "In the words of Jefferson, the clause against establishment of religion by law was intend­ed to erect a ‘wall of separation between church and state.' "

But consider that what they quote from Thomas Jefferson was inspired by diction of a Baptist preacher and Jefferson made statements that are contrary to the Supreme Court's concept of a wall of separation.

One more thought to consider: Roger Williams called the church a garden which implies peace and beauty and he called the world a wilderness. He saw the church as a place to be refreshed from the wilderness.

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[O]ur excellent Constitution . . . has not placed our religious rights under the power of any public functionary. Letter to the Methodist Episcopal Church, 1808. This statement can be seen in Writings of Thomas Jefferson, Albert Ellery Bergh, editor.