“Would you buy a used car from this man?” was a joke told at the July 1960 Democratic National Convention about Republican presidential challenger Richard Nixon; the slogan was put on a popular poster. Used car salesmen were regarded as con artists who put shiny coats of polish on cars with bad engines, fooling buyers.
 
Although the used car industry has changed (as well as politics), the slogan is still remembered and used. New York-based political journalist Noel E. Parmentel, Jr. has been credited with originating the line.
 
Used car salesmen also play in a popular computer joke: “Q: What’s the difference between a used car salesman and a computer salesman?  A: The used car salesman knows when he’s lying.”
   
   
Wikipedia: Noel Parmental
Noel E. Parmentel, Jr., was a leading figure on the New York political journalism, literary, and cultural scene during the third quarter of the 20th Century.
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(Carey McWilliams, editor of The Nation, credited Parmentel with introducing the much-quoted line about Richard Nixon, “Would You Buy a Used Car From This Man?”.)
 
11 July 1960, Capital Times (Madison, WI), “Democrats Can Party and Politic As Big as GOP” by Arthur Edson (AP), pg. 2, col. 5:
Naturally a lot of comedy was attempted, and this probably is a fair sample.
 
The Democrats, the story runs, will buy 20-second TV spots in which the picture of Vice President Richard M. Nixon, a shoo-in for the Republican nomination, is flashed on the screen.
 
While the viewer watches the picture, the announcer is supposed to intone:
 
“Would you buy a used car from this man?”
 
It may not be much, but it got a big laugh from the $100-a-platers.
     
12 July 1960, New York (NY) Times, “Democrats in Doubt: Convention Will Nominate Kennedy, But Great Issues Cause Conflicts” by James Reston, pg. 21:
The most popular joke of the convention among the Democrats is one of those glowering pictures of Mr. Nixon, with a caption reading: “Would you buy a used car from this man?”
 
14 July 1960, Aberdeen (SD) American-News, “Earl Wilson At Convention,” pg. 4, col. 5:
THE GAGS HERE WERE, naturally, anti-Republicans.
 
One was: “Would you buy a used car from Dick Nixon?”
 
Google Books
The Nation
Volume 220
1975
Pg. 34:
To put it bluntly, Nixon remains today what he was at the start of his career: a con man. The celebrated question first raised and set on its astonishing course by Noel Parmentel, incidentally a Nation contributor—“Would you buy a used car from this man?”—-says it all. But it never needed saying; it should have been obvious.
   
FOX Nation
March 06, 2012
Poll: Republicans Would Rather Buy a Used Car From Santorum
posted at 5:25 pm on March 6, 2012 by Tina Korbe
In the 1960 U.S. presidential election, an unaffiliated poster that featured a shifty-looking Richard Nixon snidely asked, “Would you buy a used car from this man?” U.S. voters suggested by their election of John F. Kennedy that they wouldn’t. Since then, the casual use of the question in discussions of political candidates has become standard, a rather fun and punchy way to measure whether voters trust pols.