“Politics is a contact sport” means that politics is rough business, like the sport of boxing. Japanese politics was called a “contact sport” in June 1960. “Politics is a contact sport” was popularized by conservative columnist James J. Kilpatrick (1920-2010), who used the saying in columns published in 1966, 1968 and 1970.
 
“Democracy is a contact sport” is used less frequently and has been cited in print since at least 1992.
 
 
Google News Archive
14 June 1960, The Gazette (Montreal, Quebec), “Political Harakiri” by Marguerite Higgins, pg. 6, col. 5:
But with millions on the streets how can the public prevent at a minimum an inter-faction fight among the Japanese who consider politics a contact sport even when it is carried on in the House of Parliament itself?
(This was also published in the Winnipeg Free Press, June 13, 1960, pg. 7, col. 3—ed.)
 
17 June 1960, Winnipeg (Manitoba) Free Press, “Beatnik Red Is Gay Chief Of Tokyo Riots” by Marguerite Higgins, pg. 7 col. 2:
He is Tokoe Onda, the acting leader of the Kamikaze-spirited Zengakoran students who have been in the vanguard of the violence that has turned Japanese politics into a bruising—and sometimes fatal—contact sport.
 
12 May 1966, The Daily Times-News (Burlington, NC), “The ‘Master’ Is Slipping” by James Kilpatrick, pg. 4A, col. 6:
WASHINGTON—Every man knows what it is to encounter a string of days when he shoulda stood in bed. These are days when it hardly pays to get up; and Lyndon Johnson has had a month of them lately.
 
This is, mind you, no particular plea for the President. He knows, better than most men, that politics is a body-contact sport. When it comes to trading punches, you give a few, you take a few, and you don’t cry over a fat lip.
 
18 January 1968, Omaha (NE) World-Herald,  “Nixon’s Night of Long Knives” by James J. Kilpatrick, pg. 18, col. 3:
To be sure, politics is a contact sport, and Mr. Nixon will not be heard to complain.
 
Google News Archive
24 July 1970, Eugene (OR) Register-Guard, “...But, on the other hand” by James Kilpatrick, pg. 16A, col. 3:
“If the President was bruised, okay, politics is a contact sport.”
(A speech from U.S. Senator Strom Thurmond—ed.)
 
Google News Archive
10 June 1977, St. Petersburg (FL) Times, “Politics is a ‘contact sport’” by Jack W. Germond and Jules Witcover (Chicago Tribune), pg. 20-A, col. 3:
WASHINGTON—A football coach at a southern high school several centuries ago used to advise his backs to run over, rather than around, their opponents in the early stages of the game.
 
‘This is a contact sport, boy,” he would shout. “You gotta give ‘em a few good licks, you gotta make ‘em think twice.”
 
14 April 1992, San Diego (CA) Union-Tribune:
Democracy is a contact sport, one that’s not particularly satisfying from the stands.
   
Google Books
Hell’s Belles:
A tribute to the spitfires, bad seeds & steel magnolias of the New and Old South
By Seale Ballenger
Berkeley, CA: Conari Press; Emeryville, CA: Distributed by Publishers Group West
1997
Pg. 91:
“In Texas, politics is a contact sport.”—Ann Richards
 
OCLC WorldCat record
Politics IS a contact sport
Author: Alan K Simpson
Publisher: Irvine, CA : Center for the Study of Democracy, 2002.
Series: Research monograph series (University of California, Irvine. Center for the Study of Democracy), 02-04.; Peltason lecture on democracy, 2001-02.
Edition/Format:   Book : State or province government publication : English
 
Google Books’
My Life
By Bill Clinton
New York, NY: Alfred A. Knopf
2004
Pg. ?:
He simply replied to all charges with a statement that he was completely independent, that he wouldn’t respond to unsubstantiated attacks or attack his opponents in return, and that he wanted to in on his own merits “or not at all.” I finally learned that phrases like “or not at all” are often used by candidates who forget that politics is a contact sport.
 
Google Books
The Dictionary of Modern Proverbs
Compiled by Charles Clay Doyle, Wolfgang Mieder and Fred R. Shapiro
New Haven, CT: Yale University Press
2012
Pg. 203:
Politics is a contact sport.
1960 Gazette [Montreal] 14 Jun.: “But with millions on the streets how can the public prevent at a minimum an inter-faction fight among the Japanese who consider politics a contact sport even when it is carried on in the House of Parliament itself?”
   
Examiner.com
Texas Democratic Party Convention: Elects new chair, maintains status quo, sadly
JUNE 13, 2012
BY: ROBERT RUIZ
(...)
As a life-long student of both history and political-science I’ve always heard the usual majority population’s mantras about the democratic process, public policy and legislation. “Democracy is a contact sport.” “Laws are like sausages, it is better not to see them being made.” “Politics makes strange bedfellows.”