The earliest known attribution of this quote was December 9, 1951, in what appears to be an op-ed piece in The Daily Oklahoman under the byline Elmer T. Peterson, [This is the Hard Core of Freedom, Elmer T. Peterson, Daily Oklahoman, 9 December 1951, 12A]. The quote has not been found in Tytler's work. It has also been attributed to Alexis de Tocqueville.
There are many variants circulating with various permutations of majority, voters, citizens, or public. Ronald Reagan is known to have used this in speeches, as reported in Loren Collins, "The Truth About Tytler http://lorencollins.net/tytler.html":
Other variants:
The American Republic will endure until politicians realize they can bribe the people with their own money.
The American Republic will endure until the day Congress discovers that it can bribe the public with the public's money.
Attributed