Mr. Walker, who featured a 1998 Saturn with more than 100,000 miles on the odometer in a 2010 campaign ad during his first run for governor, likes to talk about flipping burgers at McDonald’s as a young person. His mother, he has said, grew up on a farm with no indoor plumbing until she was in high school.

Mr. Rubio, among the least wealthy members of the Senate, with an estimated net worth of around a half-million dollars, uses his working-class upbringing as evidence of the “exceptionalism” of America, “where even the son of a bartender and a maid can have the same dreams and the same future as those who come from power and privilege.”

Mr. Cruz alludes to his family’s dysfunction — his parents, he says, were heavy drinkers — and recounts his father’s tale of fleeing Cuba with $100 sewn into his underwear.

Gov. Chris Christie of New Jersey notes that his father paid his way through college working nights at an ice cream plant.

But sometimes the attempts at projecting authenticity can seem forced.