The concept of the founders, or, rather, "fathers" of the United States, came about pretty early on. The specific term "founding fathers" came later.

On March 19, 1787, Henry Knox wrote to George Washington lobbying him to attend what became the Constitutional Convention. In it, he wrote what is thought to be the first surviving instance of Washington being called "the father of the country":

"Were the convention to propose only amendments, and patch work to the present defective confederation, your reputation would in a degree suffer—But were an energetic, and judicious system to be proposed with Your signature, it would be a circumstance highly honorable to your fame, in the judgement of the present and future ages; and doubly entitle you to the glorious republican epithet—The Father of Your Country."

The "founding fathers" were termed the "fathers" by the early 19th century. According to the Oxford English Dictionary, the earliest known instance of this comes from the article "Sketch of the Character of the Late General Schuyler", about the Revolutionary War general and later U.S. Senator from New York, Philip Schuyler. The piece was published in the February 1810 edition of the literary magazine The Port Folio.

"How few of the patriots of the revolution, how few of the fathers of the constitution, how few of all those who, by their counsels or achievements, acquired liberty, prosperity, and glory to their country, now participate in her employments and public functions!"

Thereafter, it became more and more common. As some examples, from a February 2, 1833, debate in Congress:

"The fathers of the constitution knew no other way to support the supremacy of the laws of Congress than this. They provided that all questions arising under the constitution should be referred to and decided by the judicial department of the Government."

And from an August 6, 1841, speech in Congress:

"They were not men who said one thing and meant another. They were no partisans, but patriots. They were Washingtons, Madisons, Franklins—fathers of the country, fathers of the Constitution, fathers of science and knowledge, to whom the Father of the Gods handed down from Heaven the very lightning of his power!"

The most famous use is probably from Abraham Lincoln's Gettysburg Address of 1863:

"Four score and seven years ago our fathers brought forth on this continent, a new nation, conceived in Liberty, and dedicated to the proposition that all men are created equal."

Why call them "fathers"? This likely derives from the same reason that elders and officials in the church are called "fathers". In the same era that the term was being applied to the American politicians of the Revolutionary and Constitutional period, books about the founding of religious sects used the same term (example one, example two).

That latter example even gives an explanation for the term, citing one of the Ten Commandments:

"The fifth commandment, which requires that parents be honoured and obeyed by their children, may be extended, by parity of reason, to all those, who, as they act the part of parents towards other persons, so they deserve to receive the affection, gratitude, love, respect, obedience, and assistance, and all kind offices due to parents. Hence it hath come to pass, that one of the most ancient titles of reverence paid to kings, to magistrates, to priests, to prophets, to teachers, to masters, to benefactors, and to elders, was to be called fathers."

The use of "father" in senses like this are cited by the Oxford English Dictionary going all the way back to Old English. The earliest of the relevant senses they provide go all the way back to the first millennium:

"3. A male ancestor more remote than a parent; a forefather, a progenitor; esp. the founder of a race or family"

And:

"4a. A person, esp. a ruler or superior, who provides protecting care like that of a father; a person who shows paternal kindness, or to whom filial reverence and obedience are due."

And:

"8a. An originator, inventor, or founder of something; an important male figure in the origin and early history of something. Also: a man who provides the most conspicuous, influential, or archetypal example of something."

And:

"9a. Something which gives rise to or produces another thing."

And also relevant:

"5a. Roman History. In plural. With capital initial. The senators of ancient Rome."

And:

"5b. In plural. The leading men or elders of any city or assembly. Also occasionally in singular."

The usage of all those senses, except for 5b, are all found as early as Old English. 5b dates at least to the 1500s.

It would appear, then, that calling the Founding Fathers the "fathers" had quite a lot of precedent behind it. The term "fathers" is used to refer to the elders or founders of something, which the "Founding Fathers" most certainly are.

So what of the specific phrase "Founding Fathers"? That came later. It is often attributed to President Warren Harding. However, as etymologist Barry Popik, and editor of the Yale Book of Quotations Fred Shapiro have been able to uncover, the phrase dates back to at least the late 19th century.

Barry Popik found the phrase used in 1886, in an address at the Congregationalist Church in Fairfield, Connecticut, commemorating the church's 150th anniversary. It was one of several addresses given that day, this one entitled "Patriotism in Our Churches" and delivered by Rev. Edward Anderson. While Anderson talks about the U.S. as a "Christian nation", he is clearly talking about the Revolutionary generation, since he starts out the section of the speech talking about the "sacred blood of '76". He then says that this sacred blood "was an inheritance for '61". He appears to be calling the Revolutionaries the "founding fathers", while the Civil War veterans are "the establishing sons":

"Our land has been made secure (who doubts it) because of the Christian principle that underlies it, as shown in the deeply religious phaze of our war. Are prayers of the founding fathers to be echoed in prayers of the establishing sons, for nothing?"

Fred Shapiro, editor of the Yale Book of Quotations was able to find another early instance, used on the U.S. Senate floor on June 6, 1894, recorded in the Congressional Record (page 5849 - PDF warning). It was spoken by Sen. Joseph N. Dolph of Oregon, but interestingly, he is quoting, or perhaps paraphrasing, a speech by George Reid, a politician of Australia. Perhaps the phrase was already in regular use by then, if it was being used by an Australian:

"Mr. G. H. Reid, who was received with prolonged applause, moved, 'That this meeting offers its congratulations to the American people on the triumphant election of Mr. Grover Cleveland as President of the United States of America [cheers] and regards that event as the opening up of a new epoch of freedom and human progress.' He thought that vast assemblage would confirm that resolution with enthusiastic sincerity. [Cheers.] In that magnificent electoral revolution which had effaced Harrison and placed Cleveland upon the highest pinnacle of national confidence, which had shipwrecked the Republican party and given to the Democrats their grandest opportunity, they saw born again the grand fearless spirit of the founding fathers of the American Constitution [loud cheers] who abhorred injustice, and for liberty's sake braved death in a thousand forms. [Cheers.]"

Warren Harding's role may have been to popularize it. However, with those two earlier instances, it's quite possible it already had some level of popularity. Shapiro found at least another instance dating back to 1910. As with many things, it's quite likely Harding was simply the first U.S. President to pick up on the zeitgeist, of the already-popular phrase, and subsequent presidents and politicians just continued to popularize it ever after.

Harding's earliest known usage is from a speech given on November 19, 1914, in front of the Youngstown, Ohio, Chamber of Commerce. Four days later, the speech was printed in the November 23, 1914, edition of the Steel and Iron periodical in Pittsburgh:

"The founding fathers gave us an American merchant marine which carried more than 90 per cent of our commerce across the seas. Modern lack of patriotism has given Europeans 90 per cent of our trans-oceanic trade."

Harding used it again at his Keynote Address at the Republican National Convention On June 7, 1916:

"...we ought to be as genuinely American today as when the founding fathers flung their immortal defiance in the face of Old World oppressions and dedicated a new republic to liberty and justice."

And:

"Mine is a deep conviction that the founding fathers were divinely inspired, and the wisdom of representative popular government is proven in the surpassing achievement."

cont'd...