It is understandable that Daniel Webster would have said this during the era in which he lived. So he is correct for his time, the late 18th and 19th centuries. Anarchy would have been the result in his time, and for some time after.
But the quote needs an update. Today it should read ...if the American Constitution should fail, there will be totalitarianism throughout the world. The real techniques of totalitarian rule had not been seriously developed at that point. His world was a world of kingdoms, some good, some benign and some downright malevolent. But the power to enslave in totality, through the overwhelming apparatus of an all-powerful statealthough rooted in human nature and hinted at throughout history (Egypt, Alexander, Rome)did not really come to fruition until the 20th century.
Compared to what will really happen if the American Constitution fails, anarchy is a relatively mild and even preferable option.
JOHN ADAMS, letter to Thomas Jefferson, Nov. 13, 1815