This was called The Fall of the Athenian Republic and while it makes a good sound bite, according to Snopes it is "Mostly False."
Sometimes it follows the claim that a "Law professor's analysis demonstrates that the results of the last presidential election correspond to a prediction about the downfall of democracy. " Check out the basis for how it started here:
http://www.snopes.com/politics/ballot/athenian.asp
And for those who've seen this pop up again and again, I found this humorous:
"The item cited above began circulating on the Internet since shortly after the 2000
[font=source sans pro, sans-serif]U.S. presidential[/font] election, reappeared briefly after the 2004 presidential election, saw a strong resurgence in a modified form which replaced the names "Bush" and "Gore" with "McCain and "Obama" after the 2008 presidential election, and was circulated again after the 2012 election in a shortened version with the names "Obama" and Romney" replacing the original's "Bush" and "Gore."