“I believe in the two-party system—one on Friday night and one on Saturday night” is a jocular political saying that has been printed on many images. “Overheard on the elevator: ‘I believe in the two-party system—one on Friday night, and one on Saturday night’” was printed in the Calgary (Alberta) Herald on November 2, 1946.
     
   
Newspapers.com
2 November 1946, Calgary (Alberta) Herald, “The Scrap Book” by Beverly Gray, pg. 4, col. 4:
Overheard on the elevator: “I believe in the two-party system—one on Friday night, and one on Saturday night.”
 
Newspapers.com
1 March 1947, The Daily Tar Heel (University of North Carolina, Chapel Hill, NC), “Early Political Action Is Good Regardless of Political Disputes” by Eddie Allen, pg. 2, col. 2:
It is a foregone conclusion that the average Carolina student is a firm adherent of the two-party system, i.e., one Friday night and one Saturday night.
 
24 March 1961, Elmira (NY) Star-Gazette,  “Evenin’ Neighbor” by Peggy Gallagher, pg. 13, col. 1:
It (a card—ed.) read: “I am in favor of a two-party system—one on Friday and one on Saturday—both at your house, you d—- Republican.”
   
Google Books
Doc Blakely’s “Push Button Wit”
By James Blakely
Houston, TX: Rich Publishing Company
1986        
Pg. 109:
We’re great believers in the two party system - one on Friday and one on Saturday.
 
Google Groups: bit.listserv.politics
how to re-elect the president
todd pukanecz
Dec 19, 1991, 3:08:15 PM
(...)
>work with a viable candidate of your party preference. (I am a firm
>believer in the two party system, one on Friday and one on Saturday).
   
Google Books
Garfield’s Guide to Everything
By Jim Davis
New York, NY: Ballantine Books
2004
Pg. 96:
Some people believe in the two-party system—one on Friday and one on Saturday.
 
Twitter
SarahElizaGold
@CHADDINGTON402
I believe in a two party system one on friday and one on saturday!!!!!
11:55 PM · May 27, 2009·Twitter Web Client
   
Twitter
Ryan Humbert
@ryanhumbert
I believe in a 2 party system—One on Friday and one on Saturday!
11:55 PM · May 27, 2009·Twitter Web Client
   
Twitter
Sara
@lollypoplawyer
“democrat,republican…I guess I believe in a two party system; one on Friday and one on saturday!” 😉
12:05 AM · May 28, 2009·Twitter Web Client
 
New Jersey Monthly
Candid Candidate: Presidential Pig Farmer Henry Krajewski
Pig farmer Henry J. Krajewski wanted our votes—and he’d promise free beer to get them.
By Jim Wright | | February 10, 2016
Who is New Jersey’s most memorable and (probably) least qualified presidential candidate ever?
 
In almost any category except for vote-getting, it was tough to beat Henry J. Krajewski, a Secaucus pig farmer and tavern owner who ran for president as a third-party candidate in 1952, 1956 and 1960.
(...)
Joe McKay of North Haledon, the son of a pig farmer and a family friend, remembers stapling “Krajewski for President” posters on telephone poles near the tavern.
“Henry used to say he believed in the two-party system—one on Friday nights and one on Saturday nights,” McKay recalls.
 
Reddit—3amjokes
Posted by u/VERBERD October 23, 2020
I believe in the 2 party system….
One on Friday night and one on Saturday night.