Make out has been used with a sexual meaning since 1939.
The third edition of the NOAD reports the meaning of make out is, informally, "engage in sexual activity", "make progress", and "fare".
I was skeptical that the question "Would you buy a used car from this man?" as a generic expression of doubt about someone's reliability originated as a rhetorical question about Richard Nixon. But an Elephind search gives some credance to the idea. The earliest relevant match for the phrase "buy a used car from" in that newspaper database is from the Tom Henderson, "Convention Sideshow," in the Coronado [California] Eagle and Journal (July 21, 1960) (roughly three months before the 1960 presidential election, in which John Kennedy defeated Nixon):
One of the big questions in the minds of everyone who attended the Democratic National Convention last week in the Los Angeles Sports Arena is, "How the devil are they going to get all those balloons off the ceiling?"
It took a good organization to win the nomination, as was evidenced by the ubiquitous machine of Kennedy as compared to that of the "What, me worry?" kid, Mad Magzine's Alfred E. Neuman, whose placards were seen about the arena proclaiming the motto, "Integrity — Absurdity." Alfred didn't gt a single vote. Even Orval Faubus got half a vote.
Nixon’s picture also came into the scene, a picture of the Vice President at his grimmest over a caption asking, "Would you buy a used car from this man?"
Some notable Republicans attended the Democratic pow wow, but only Mayor Poulson of Los Angeles got as far as the platform. He gave the welcoming address.
So the place of origin of "Would you buy a used car from this man?" as a way to express doubt about a person's trustworthiness and integrity may indeed have been the Democratic National Convention of 1960, where some anonymous Democratic operative used it as a provocative challenge to Richard Nixon's honesty and character.
Interestingly, Republicans attempted to float a similar question about Lyndon Johnson in the 1964 presidential election, but abandoned it when it failed to gain traction with prospective voters, according to a syndicated column by Jack Wilson published on October 28, 1964:
Notice that the Republicans have dropped that line, "Would you buy a used car from LBJ?" They got a backlash—turns out there were more used car dealers than customers.
By 1965, the expression was familiar enough to U.S. audiences to be used widely in nonpolitical contexts. For example, country-western singer Norma Jean Beasler had a hit song in 1965 called "I Wouldn't Buy a Used Car from Him," which reached number 8 on the C&W charts. The song is about an untrustworthy former sweetheart and doesn't seem to allude to Nixon (or Johnson) at all.
When Richard Nixon ran for president in 1968 (against Hubert Humphrey), the old question became popular once more. For several weeks before that election, the Columbia [University, New York] Spectator ran an advertisement for a campaign button that read "I wouldn't buy a used car from either one." Maybe that's how Nixon won.
Best Answer
I would distinguish between instances of "dead man walking" in the sense of "a man walking as if he were dead" and instances of the same phrase used in the sense of "man condemned or in some inescapable way doomed to die soon." Writers and speakers might use the phrase in the former sense in situations where the "dead man" is purposeless and joyless, but not necessarily headed for imminent death. Such a person might be a "dead man walking" for years.
In prison lingo, "dead man walking" seems initially to have referred to a condemned person walking to the place of execution. It may, however, have been broadened subsequently to apply to anyone living in prison under a death sentence. (I haven't found any information on this point.)
There is an interesting early instance of the wording used in the sense of "man doomed to die" (although not following conviction of a crime). From "A Soldier's Doom: The Horrible Result of a Bite from a Mad Horse," in the [Monmouth, Illinois] Warren County Democrat (January 17, 1895):
Somewhat similar is this instance from "Wife Slayer Says He's Already 'Dead Man'," in the Richmond [Kentucky] Daily Register (March 16, 1920):
But most relevant to the modern prison sense of "dead man walking" is this item in a "New Books" column in the [Kalamazoo, Michigan] Focus News (December 15, 1978):
Campbell's book, which is subtitled "Teaching in a Maximum Security Prison," seems to be mainly about the experience of being a teacher in that setting, rather than particularly involving work with condemned prisoners. Nevertheless, the usage cited in Robin Hamilton's answer is exactly on point. Here is a fuller version of the excerpt that appears in that answer [combined snippets]:
From this excerpt, it appears that the slang phrase was already in use in the prison at San Quentin (California) by 1978. And if Campbell was writing about his teaching experiences at a different prison, the San Quentin incident may have been considerably earlier than 1978.