Dance (especially the tango) has been called “a three-minute love affair (with a stranger)” and “a three-minute romance.” It’s not known who originated the descriptions.
 
“Think of every dahnse as a three-minute love affair” was cited in a 1988 book. “With swing, you can have a three-minute romance, no strings attached,” Terry Monaghan, a dance historian, said in 1997. Dance legend Frankie Manning (1914-2009) was reported in a 2002 newspaper article for calling swing dance a “three-minute affair with no strings attached.” Monaghan wrote in “Frankie Manning, the Ambassador And Master of Lindy Hop, Dies at 94,” the April 28, 2009 New York (NY) Times obituary:
 
“When questioned about the apparently irresistible allure of the Lindy, Mr. Manning invariably described it as ‘a series of three-minute romances.’”
 
Manning could have said “three-minute affair/romance” as early as the 1930s, but early print citations have not been located.
 
   
Wikipedia: Frankie Manning
Frankie Manning (May 26, 1914 – April 27, 2009) was an American dancer, instructor and choreographer. Manning is considered one of the founding fathers of Lindy Hop.
   
Google Books
The Object of My Affection
By Stephen McCauley
New York, NY: Washington Square Press
1988    
Pg. 68:
She spoke with a heavy Brooklyn accent, but she always pronounced dance as “dahnse,” as Ginger Rogers in jodhpurs might have prounced it.
 
“Think of every dahnse as a three-minute love affair,” she’d say, posed with her eyes shut.
     
20 April 1997, New York (NY) Times, “Generation X Moves to Swing City” by Andrew Jacobs, pg. 43:
’‘With swing, you can have a three-minute romance, no strings attached,’’ said Terry Monaghan, a dance historian, who is writing a book about Harlem’s Savoy Ballroom, where the Lindy was popularized in the late 1920’s and early 30’s. ‘‘If you like your partner, you can have another spin,’’ he added. ‘‘If not, you move on. Over all, it’s a civilized way of interacting with other people, something that has been lost in this country for decades.’‘
 
30 January 1998, Austin (TX) American-Statesman, “Tango: It’s an Argentine thing. The dancers understand” by Jeanne Claire van Ryzin, pg. 30:
Perhaps no other dance has inspired so many metaphors or remained so irresistible. Tango has been described as a three-minute love affair, the “chess” of all dances, a dance of love and death, a vertical expression of a horizontal desire, a sad thought that can be danced, the idiom of immigrants, and a secret danced by two.
   
2 November 2001, Daily Herald (Arlington Heights, IL), “Dance. Chicago” by Barbara Vitello, sec. 6, pg. 9, col. 2:
But they all pale in comparison to the three-minute romance that is the tango.
 
19 January 2002, Press & Sun-Bulletin (Binghamton, NY), “Night Spots: Swing dance club offers no-strings-attached fun” by Sarah Miller, pg. C1:
That’s not to say you can’t make it a romantic thing. Dance legend Frankie Manning (get this—he shows up on no less than 6,500 Web sites) is reported to have said swing dancing can be a “three-minute affair with no strings attached.” Manning is still dancing and going strong at 87.
   
MPR (Minnesota Public Radio)
The “three-minute love affair”
by Bob Collins, Minnesota Public Radio
November 18, 2005
No other dance connects people more closely than the Argentine tango, emotionally as well as physically.
 
Mandragora Tango     
November 30, 2006
Contest to write Mandragora’s Motto in 10 words or less!
(...)
Manragora Tango. Cross generational. Argentine Tango (music of the “3 minute affair”). (Margaret Kittelson)
(...)
Mandragora Tango: Translating the mysteries of your soul into an evening filled with 3 minutes romances (Bill Boyt)
 
San Francisco (CA) Bay Guardian
The three-minute romance
09.26.08 - 12:32 pm | Molly Freedenberg
PrintPrint  
By G. Martinez Cabrera
(...)
For me, I’m still deciding if I should go back. After asking people why they took the time out of their lives to learn what seems like a pretty technical dance, each person, in his or her own way, said the same thing: connection. “It’s a three-minute romance,” one of the dancers told me. And that’s the line that has stuck with me since.
   
28 April 2009, New York (NY) Times, “Frankie Manning, the Ambassador And Master of Lindy Hop, Dies at 94” by Terry Monaghan, pg. B16:
Frankie Manning, a master of swing-era dance who went from the Savoy Ballroom in Harlem to Broadway and Hollywood, and then after a long break enjoyed a globe-trotting second career as an inspirational teacher and choreographer of the Lindy hop, died on Monday in Manhattan. He was 94 and lived in Corona, Queens.
(...)
Excelling in what quickly became first America’s and then the world’s most popular participatory form of jazz dancing in the 1930s and ‘40s, Mr. Manning led the way in giving the Lindy hop professional expression. The dance, which enables both partners to improvise rhythmically at the same time, has had enduring appeal as both a social and a performance dance, sweeping aside hierarchical, class, ethnic and gender conventions. When questioned about the apparently irresistible allure of the Lindy, Mr. Manning invariably described it as “a series of three-minute romances.”
 
23 May 2009, New York (NY) Times, “Honoring the Man Who Helped Make The Lindy Hop” by Glenn Collins, pg. A14:
He soon became a dapper, charismatic Pied Piper of the Lindy, which he described as “a series of three-minute romances,” insisting that it was a social leveler that swept aside ethnic, class and gender traditions.
 
Google Books
Understanding Global Cultures:
Metaphorical Journeys Through 31 Nations, CLusters of Nations, Continents, and Diversity
By Martin J. Gannon and Rajnandini Pillai
Thousand Oaks, CA: SAGE Publications, Inc.
2013
Pg. 565:
I notice that many tangueras, like me, close their eyes as they give themselves over to what is summarily called a “three-minute love affair with a stranger.”
   
Twitter
Slicktor
‏@slicktorVictor
Think of every dance as a three minute love affair! #dance #love
7:42 AM - 16 Oct 2014
 
Twitter
Stephen Magagnini
‏@SteveMagagnini
Looking for a three minute love affair without commitment?West Coast swing draws dancers young and old to Sacramento
3:38 PM - 15 Feb 2016
 
Google Doodle
May 26, 2016
Frankie Manning’s 102nd birthday
(...)
Frankie Manning often described the dance as a “series of three-minute romances.” Here’s to the Ambassador on what would have been his 102nd birthday, and his role in creating for countless people—even if it lasted only three minutes—a moment that transcended the world around them.