"And what, Mr. President, do you suppose it is?"

Henry Clay concluded his speech of January 29, 1850 introducing his compromise resolutions by stirring the patriotic feelings of his auditors. He did so by invoking that great symbol of the Union, George Washington. And he invoked Washington by “relating an incident, a thrilling incident” that was both improbable and calculated to encourage his listeners to suspend their disbelief.

That very morning, Clay related, a man came to his room. Unaware that Clay was just about to give a speech seeking to save the Union, the man offered him an object that he described as “a precious relic.”

He then drew out of his pocket, and presented to me, the object which I now hold in my hand.

Here Clay dramatically thrust out his hand. Addressing Vice President Millard Fillmore, Clay continued:

And what, Mr. President, do you suppose it is?

It is a fragment of the coffin of Washington – a fragment of that coffin in which now repose in silence, in sleep, and speechless, all the earthly remains of the venerated Father of his Country.

Was it portentious that it should have thus been presented to me? Was it a sad presage of what might happen to that fabric which Washington's virtue, patriotism, and valor established?

No, sir, no. It was a warning voice, coming from the grave to the Congress now in session to beware, to pause, to reflect before they lend themselves to any purposes which shall destroy that Union which was cemented by his exertion and example.

Sir, I hope an impression may be made on your mind, such as that which was made on mine by the reception of this precious relic.

A brief coda followed:

And, in conclusion, I now ask every Senator, I entreat you, gentlemen, in fairness and candor, to examine the plan of accommodation which this series of resolutions proposes, and not to pronounce against them until convinced after a thorough examination.

This site suggests it is conceivable that Clay was given a fragment of George Washington's coffin – or at least that such fragments or purported fragments existed and were in circulation:

George Washington Purported Coffin Fragment and Memorabilia. Including a photograph of his tomb, a colored engraving, card with Washington's coat of arms, overall: 15 1/2" x 16" (sight), matted together and framed, Together With a photograph of a group outside his tomb, 8" x 10". When George Washington was originally buried, his body was placed in a wooden casket which was then placed in a closed vault. In 1837, his body was removed from the wooden casket and re-interred in a new marble sarcophagus. The exhumation was witnessed by a number of neighbors and celebrities of the day. The old wooden casket was broken into pieces and presented to those in attendance. This piece, measuring 1 1/2 " x 3/4 " x 3/4 ", is attached to a newspaper clipping (c. 1837) and is mounted with prints of Washington and his gravesite. The newspaper article reads: Some of Washginton's Coffin [From the Milledgeville (Ga.) Union and Recorder]." We held in our hand yesterday a piece of the black walnut coffin in which George Washington, the "Father of His Country" was buried. It was in the possession of H.V. Sanford and about the size of a woman's hand. Mrs. General John W.W. Sanford, formerly of this society, was a lady of great refinement and cultivation, a great traveler, and of fine education. She was present when Washington's coffin was exhumed and procured several pieces of the coffin much larger then [sic] the one handled yesterday, which are now in the possession of a sister of H.V. Sanford. The pieces are about half an inch in thickness, and on account of age, and the many years that they were in the ground, are very light."