John F. Kennedy was an heir to a fortune worth hundreds of millions, yet his portrait adorned the living room walls of some of the nation’s poorest families. Nelson Rockefeller was the grandson of America’s richest oil magnate, but he won backslaps and hugs when, as governor, he showed up at New York’s ethnic eateries.

George H.W. Bush, in contrast, came from a fortune nowhere near as large, yet when Texas Gov. Ann Richards described the 1988 Republican presidential nominee as having been “born with a silver foot in his mouth,” the image stuck.

Mitt Romney, who grew up wealthy as the son of the chief executive of American Motors and who made his own fortune in the private-equity business, saw his Republican presidential campaign poll numbers tumble after former House speaker Newt Gingrich began portraying him as a detached millionaire who made his fortune by cutting jobs as much as by creating them.

Will that picture of the former Massachusetts governor stick? Why do Americans admire some wealthy politicians, but resent others?

POLL: Do you admire these wealthy Americans?

One simple answer is that Americans love a self-made man and tend to be suspicious of those born with money. But for a people of a nation founded in rebellion against rule by men with inherited wealth, Americans have happily supported many politicians — Rockefellers, Kennedys, Bushes — who grew up rich.

As Romney has discovered, some wealthy politicians win acceptance from people who are just scraping by, while others get tagged as hopelessly out of touch.

The most important tool wealthy politicians have relied on to win over the public is pure force of personality — and that often includes a gift for self-deprecating humor.

Theodore and Franklin Roosevelt both came from big money, yet the presidents’ larger-than-life affability and celebrity won them admiration across class lines. Kennedy came to elective politics with a dramatic backstory as a war hero that canceled out most suspicions that he might be a rich dandy.

Romney, however, despite several attempts to reshape his message, remains awkward in his discussions about money. When he handed $50 to an unemployed South Carolina woman who told him her hard-luck story, referred to his $370,000 in income from speaking fees as “not very much,” or challenged opponent Rick Perry to a $10,000 bet, Romney unintentionally enriched the narrative that Gingrich is peddling, in which Romney lives in a world “of Swiss bank accounts and Cayman Island accounts and automatic $20 million a year income with no work.”

The popular image of Romney’s wealth is muddled because he both grew up rich and made his own fortune. One reason former pizza magnate Herman Cain rocketed to the top of the charts earlier in this primary season is that he evidently pulled himself up by his own bootstraps — the classic American success story. The same goes for New York Mayor Michael Bloomberg, who started out as a parking-lot attendant and is now listed by Forbes as the nation’s 12th-richest person.

“If Romney is seen as contributing to economic growth, that kind of wealth is very much admired,” says Leslie McCall, a Northwestern University sociologist who is completing a study on American attitudes toward income inequality. “But if it’s obtained through means that aren’t sensitive to the middle class and the poor, that’s another story.”

Even if Romney successfully portrayed himself as a job creator, he may also be victim of a fact that is beyond his control: It turns out that timing is an important factor in determining whether wealthy candidates succeed. McCall’s research suggests that Americans’ attitudes toward the rich wax and wane, with resentment against the wealthy surging especially when the rich are doing well at a time when the average family is struggling.

Romney’s friends and aides say his life’s work disproves the cartoon image of the rich kid who grew up without much exposure to middle-class America. They say his work at Bain Capital helped businesses that employ thousands of people. And they say he was raised with a keen sense of the value of a dollar — just last week, Romney and his wife, Ann, sent an aide to pick up their breakfast at McDonald’s rather than shell out for an expensive hotel meal.

Nonetheless, Romney has repeatedly stubbed his toe against the boundary of Americans’ tolerance of the very rich. The fuzzy nature of that border is apparent in the ongoing debate within the Republican Party, which has long trumpeted the idea that individual success is the breeding ground for broader well-being.

Primary voters are now being asked to figure out whether it was merely gauche when Romney boasted that he was “happy that [Ted Kennedy] had to take a mortgage out on his house to ultimately defeat me” in a Massachusetts Senate race or if Romney was exposing himself as a vulture capitalist.

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“Handing out cash to people — that’s just bad manners,” says Nelson W. Aldrich Jr., a cousin to the Rockefellers who has written several books on American attitudes toward wealth. “Romney has a tin ear that comes from having lived in a bubble his whole life. He never worked in a business full of middle class and poor employees. He seems nervous about the issue of money.”

Aldrich says criticism of Romney’s $20 million in income from investments last year misses the mark: “What matters is not his income, but his wealth. Romney is the hereditary rich. That money is not going to leave his family when these people croak. It doesn’t get used to create jobs for others; it gets used to create advantages that are purchasable by inherited wealth. We’re not talking about yachts, but tutors, the best schools, the cultivation of civilized behavior. Income is what makes possible an equal-opportunity society. Wealth is what prevents it.”

The Romney campaign declined to answer questions for this article; it instead passed along this statement the candidate made in last Monday’s debate: “I will not apologize for having been successful. I did not inherit what my wife and I have, nor did she. What we have — what I was able to build — I built the old-fashioned way, by earning it, by working hard. And I was proud of the fact that we helped create businesses that grew, that employed people. And these are not just high-end financial jobs.”

Romney says he gave all the money he inherited to his children and charity. He told a Univision interviewer last week that his assets add up to about $150 million to $200 million.

Romney’s aides last week handpicked eight struggling Floridians to meet with the candidate in a Tampa hotel conference room to tell stories the candidate later called “human tragedies.”

Wearing jeans and a casual windowpane shirt and carrying only a yellow legal pad and a pen, Romney listened as Todd Swift, a consultant, described how his condo investments went bust.

“Yeah,” Romney said, taking notes. “That is tough. Thanks, Todd, for sharing that.”

Candice Tamm­ney, who is remaining in her house only until the bank kicks her out, told of losing her job and exhausting all her savings. “I did everything I could,” she said, before she had no choice but to stop paying her mortgage.

Romney took notes, rattled off some unemployment statistics and asked ­Tammney about her efforts to find work.

Through one tale of woe after another, Romney never spoke of his own experiences, never mentioned the years he had spent counseling struggling people as a lay pastor in the Mormon church. At the end, he shook the Florida voters’ hands and offered his e-mail address. Romney offered no hugs, no back and forth, no experiences or stories related to the struggles he’d heard about.

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In 1992, when then-President George H.W. Bush flashed an amazed look upon seeing a demonstration of a supermarket price scanner, he was unfairly slammed as a rich guy so removed from ordinary life that he had never seen a staple of daily existence. In fact, Bush was expressing wonder over a new, advanced scanner, but the inaccurate reporting hit a nerve with voters who perceived Bush as detached.

Bush’s rich-guy reputation was so enduring that his son, George W., set out to create a wholly different story line — avoiding his Ivy League alma maters and Maine coast family compound to highlight his down-home Texas persona, a regular guy who spoke, acted and dressed differently from his Connecticut Yankee father.

President George W. Bush’s 2004 reelection campaign turned the tables on his wealthy opponent, Sen. John F. Kerry, who was pictured in a Bush-Cheney TV ad windsurfing off Nantucket, blowing to and fro as an announcer reeled off his waffling positions on a series of issues.

Beyond personality, the way the wealthy make and use their fortunes plays a role in how they are perceived. Microsoft co-founder Bill Gates and investment mogul Warren Buffett enjoy broad popularity in good part because they are associated with businesses that created opportunity for others and decided not to pass their billions down to their children, instead giving away the bulk of their money to charity.

Gates and Buffett follow Andrew Carnegie’s admonition to the rich to avoid the flashy high life. The “duty of the man of wealth,” Carnegie said in 1889, is “to set an example of modest, unostentatious living, shunning display or extravagance; to provide modestly for the legitimate wants of those dependent upon him; and, after doing so,” to use the rest of their money for “the most beneficial results for the community.”

Yet even as Americans admire those who give it away, a consistent majority of the public remains suspicious of estate taxes, believing that if you make a lot of money, you ought to be able to give it to your children. “There’s a double standard in our psyche that hasn’t changed through our history,” says Arizona State University law professor Marjorie Kornhauser, who has written about how U.S. tax policies reflect our confusion over the morality of money. “We have very mixed attitudes toward the rich.”

Romney’s wealth is “ambiguous,” she says. “It’s not 100 percent clear to most people whether he created jobs or destroyed them, and he actually created some and lost some.”

One of the most radical ideas in the American Revolution was to take power from inheritors of wealth and focus instead on equality of opportunity. The founders were determined to dismantle the practices of monarchy — “its hierarchy, its inequality, its devotion to kinship,” historian Gordon Wood wrote in his 1993 Pulitzer Prize-winning book, “The Radicalism of the American Revolution” (which Gingrich has praised lavishly).

The new country would not guarantee equality of income, but rather equality in the sense that “no one was really better than anyone else,” Wood wrote.

Americans become more sensitive to that point during periods of high unemployment and severe income inequality, McCall’s research has found.

“I’m finding that what matters most is the context of wealth,” she says. “Romney is a victim of being seen as out of touch in a time when there are questions about whether the rich have been contributing productively to the welfare of the country.”

In the mid-1990s, when the country experienced a relatively jobless recovery similar to today’s, the popular culture was full of depictions of investment bankers and hedge fund executives as greedy, destructive forces. “That was also the time of Ross Perot’s popularity and a focus on the plight of the middle class,” McCall notes.

Later in the ’90s, by contrast, the rich were celebrated as the economy grew and unemployment dropped to 4 percent.

As real estate tycoon Donald Trump put it in a 2009 interview with Fox News, during hard times, “it is open season” on the rich. “But I think it will straighten out, and, ultimately, people want to be rich. And that’s part of the American way.”

Staff writers Philip Rucker and Rosalind S. Helderman contributed to this report