In 1896, Democratic Presidential candidate William Jennings Bryan made reference to trickle-down theory in his famous "Cross of Gold" speech:
There are two ideas of government. There are those who believe that if you just legislate to make the well-to-do prosperous, that their prosperity will leak through on those below. The Democratic idea has been that if you legislate to make the masses prosperous their prosperity will find its way up and through every class that rests upon it.
The Merriam-Webster Dictionary notes that the first known use of trickle-down as an adjective meaning "relating to or working on the principle of trickle-down theory" was in 1944, while the first known use of trickle-down theory was in 1954.
After leaving the Presidency, Lyndon B. Johnson, a Democrat, alleged, "Republicans [...] simply don't know how to manage the economy. They're so busy operating the trickle-down theory, giving the richest corporations the biggest break, that the whole thing goes to hell in a handbasket." 
Speaking on the Senate floor in 1992, Sen. Hank Brown said, "Mr. President, the trickle-down theory attributed to the Republican Party has never been articulated by President Reagan and has never been articulated by President Bush
and has never been advocated by either one of them. One might argue whether trickle down makes any sense or not. To attribute to people who have advocated the opposite in policies is not only inaccurate but poisons the debate on public issues."
Thomas Sowell claimed that, despite its political prominence, no trickle-down theory has ever existed among economists.
 In response, many critics referred him to Stockman's remarks to Greider. Sowell replied in his newspaper columns. Stockman himself had not proposed or advocated the alleged theory, so Sowell rejected him as an example of someone who had done so. Additionally, Stockman had not specifically named anyone who, or quoted a source that, advocated the theory although he did claim that the theory was being adhered to by the Reagan administration. Sowell replied that Stockman "was not even among the first thousand people to make that claim" but that "not one of those who made the claim could provide a single quote from anybody who had advocated a 'trickle-down theory.