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1990s
                                    
            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
        
                                        
                                        The Public Square, by Richard John Neuhaus, First Things 1996 
1990s
                                    
Source: speech during a meeting in the R. Barbosa High School
                                        
                                         Letter to The Times http://coreyrobin.files.wordpress.com/2012/07/hayek-letter-to-the-times-july-11-1978.pdf (11 July 1978), p. 15 
1960s–1970s
                                    
Creation seminars (2003-2005), The Garden of Eden
Source: Sailing the Wine-Dark Sea: Why the Greeks Matter (2003), Ch.IV The Politician and the Playwright: How to Rule
The Theory of Democracy Revisited (1987), 1. Can Democracy Be Just Anyting?
                                        
                                        “Much more than periodic voting” – UN Independent Expert calls for more direct democracy worldwide  http://www.ohchr.org/en/NewsEvents/Pages/DisplayNews.aspx?NewsID=20482&LangID=E. 
2016, “Much more than periodic voting” – UN Independent Expert calls for more direct democracy worldwide
                                    
 
                            
                        
                        
                         
                            
                        
                        
                         
                            
                        
                        
                        