While I certainly can't claim credit for it, I have been one to use it (and its larger cousin Rationalistic Totalitarian Democracy) quite often on this forum. They have an interesting history.
First of all we have John Randolph of Roanoak, Calhoun and others early on in Congress shouting down "King Numbers" when majoritarian values become promoted as virtues. But the amplified version was a favorite of Hayek and was used in Chapter Four of The Constitution of Liberty but I have heard other origins.
Lately, reading a wonderful new book by Fareed Zakaria entitled The Future of Freedom, Illiberal Democracy at Home and Abroad, I came across this:
Page 65He goes on to foot note that quote to Jacob L Talmon, The Origins of Totalitarian Democracy London: Seeker and Warburg, 1955.
The social forces that sped the United Kingdom along were weak in France, which had a dependent aristocracy and merchant class. ...So post revolutionary France embraced democracy without a developed tradition of constitutional liberalism. Liberty was proclaimed in theory rather than being secured in practice (by a seperation of powers and by the strength of nonstate institutions such as private business, civil society and an independent church). The revolutionaries believed that Montesquieu was utterly misguided in asking for limited and divided government. Instead the absolute power of the King was transferred intact to the new National Assembly, which proceeded to arrest and murder thousands, confiscate their property, and punish them for their religious beliefs, all in the name of the people. Some scholars have aptly call the Jacobin regime "totalitarian democracy." It is the first example in history of modern illiberal democracy.
Now as Hayek was writing in 1960 that major work of his, perhaps he had used the phrase elsewhere, earlier, I don't know.
But it is an important concept with a longer tradition of being realized than we might at first suspect.