In a nation of 319 million people, America’s 2016 presidential election could well come down to a rematch between two of its greatest modern political families: the Bushes and the Clintons.

Hillary Rodham Clinton is crushing it in polls for the Democratic nomination. The former secretary of State, senator, and first lady leads her nearest potential competitor – Vice President Joe Biden – by an average of 44 percentage points in major polls. And she hasn’t even taken the first formal step toward running. In terms of fundraising and organizing, though, Mrs. Clinton is all in.

Jeb Bush, the son and brother of former presidents, is at or near the top of the vast potential Republican field in most polls. The former governor of Florida has some commanding advantages: the Bush family’s killer Rolodex and, flowing from that, the ability to raise vast sums of money. At one recent fundraiser, tickets went for $100,000 a pop.

Like Clinton, Mr. Bush has lived and breathed politics at the highest level for decades. For both, politics is the family business. Both epitomize “establishment.”

Many Americans, when asked, recoil at the prospect of another Clinton-Bush presidential race, an echo of the 1992 contest that pitted then-Arkansas Gov. Bill Clinton against President George H.W. Bush. The United States was founded in rebellion against royal privilege and inherited status. As children, Americans are told that anyone can grow up to be president. And yet throughout US history, voters have regularly gravitated toward “brand name” political families.

“There’s this paradox in the American body politic,” says Barbara Perry, a presidential scholar at the University of Virginia in Charlottesville. “We always say that we want someone who’s up from the log cabin, but we are drawn to the wealthy, noblesse oblige candidates as well.”

How did we reach this moment, when two A-list political families – one with generations of wealth, the other of humble origins but now just as privileged – could end up facing off for the presidency?

It’s no accident. Citizens United, the Supreme Court ruling that opened the floodgates of outside spending on campaigns, has raised the stakes exponentially for presidential fundraising. That gives a huge advantage to candidates with entree to big money.

So far, Clinton has effectively cleared her party’s field. Bush hasn’t, but even his competitive status is telling: What other politician, eight years out of statewide office, could pull that off? It’s all about the Bush name. And in a presidential cycle in which the major-party candidates may have to raise $2 billion each – almost double what President Obama and Mitt Romney raised in 2012 – viability begins with money.

That 2016 could feature two dynastic titans is also the product of deliberate planning. With the Bushes, “this is conscious, intergenerational preparation,” says Cal Jillson, a political scientist at Southern Methodist University in Dallas. “Go back to Senator Bush out of Connecticut, and then everybody after that.”

He is referring to the family patriarch, Rebublican Sen. Prescott Bush, father of George H.W. and grandfather of George W. and Jeb.

With the Clintons, the presidential gleam is visible in the iconic photograph of a teenage Bill Clinton shaking hands with President John F. Kennedy in 1963, when Clinton was a delegate to the American Legion Boys Nation in Washington, D.C.

“Hillary married that, in a conscious sort of way, and has prepared herself,” says Mr. Jillson.

The parties’ establishments and the news media are complicit. They naturally gravitate toward brand-name politicians during the so-called invisible primary – the early period of fundraising and buzz-generation, up until the start of the actual primaries. So do many voters, which seems ironic given their distrust of government and politicians.

“There is some kind of strange comfort in going for the same thing, even though that means you’re going for people from the system,” says Julian Zelizer, a historian at Princeton University.

“People are searching for someone who might be able to work through the gridlock in Washington, who might be able to survive in a very contentious and difficult political system. That kind of experience, whether it’s through family or through official positions, becomes attractive to people.”

There are no sure things in politics. But in the race for the Oval Office, Clinton and Bush have an enormous head start.

• • •

American political dynasties are older than the republic itself. Samuel and John Adams, second cousins, were signers of the Declaration of Independence. Upon the founding of the United States, John Adams served two terms as the first vice president, then one term as the second president.

The Adamses sealed their identity as an American “royal family” of sorts when son John Quincy Adams was elected the sixth president in 1824. But long before John Quincy rose to the top, the Adams “brand” already had a monarchist tinge. John Adams in fact vehemently opposed hereditary monarchy and titles, according to biographer David McCullough. But Adams didn’t do his image much good early in his vice presidency when he suggested that George Washington be called “His Majesty the President.” The Senate settled simply on “President of the United States.”

But Adams did believe in a strong executive. And when he ran to succeed Washington as president, the Republican press mocked the portly Adams as “His Rotundity.”

“Were Adams to be elected, warned the Boston Chronicle, the principle of hereditary succession would be imposed on America, to make way for John Quincy,” Mr. McCullough writes in his book “John Adams.” With Thomas Jefferson, Adams’s opponent in the election of 1796, the Boston paper said that no one need worry since Jefferson had only daughters, McCullough notes.

Adams beat Jefferson anyway. But four years later, the populist Jefferson deprived Adams of a second term. In 1824, John Quincy Adams ran for president, and the “monarchist” charge returned. “The father whom he so much admired was to a considerable extent a liability,” says Fred Kaplan, author of “John Quincy Adams: American Visionary.”

John Quincy won – barely. As in the election of 2000, when another son of a one-term president ran for the job himself, the election of 1824 produced an inconclusive result (which was decided by the House of Representatives). But unlike George W. Bush, who won a second term, John Quincy Adams lost reelection. The charge of “elitist” and even “crypto-monarchist” bit again.

The John Quincy story matters, not only because it shows how fears of hereditary succession lingered in the US decades after its founding, but also for its relevance to the Bush family. The second President Bush felt a kinship to John Quincy, and kept a portrait of the sixth president in the private dining room off the Oval Office.

“I hung it as an inside joke with Dad,” who had teased him about “Q,” writes George W. Bush in his memoir.

Still, the comparison between Q and W is easily overdrawn. In a way, John Quincy was more like the first President Bush than the second. John Quincy and George H.W. each brought a long, distinguished résumé of federal government service to the presidency. Indeed, in George W.’s first presidential race, his dad was a net asset, according to an August 2000 Gallup/CNN/USA Today poll archived by the Roper Center at the University of Connecticut.

Twenty-five percent of Americans said that former President George H.W. Bush made them feel more favorably toward George W. Bush, versus 15 percent who said the father made them less favorable toward the son, the poll found.

Today, polls show a decided tilt against the dynastic element of Jeb Bush’s expected candidacy. In January, 34 percent of registered voters said that the presidencies of Bush’s father and brother make them less likely to support Jeb, versus only 9 percent who said they make them more likely, according to an ABC News/Washington Post poll.

Hillary Clinton, in contrast, gets a net boost from her husband, according to the same poll. Some 24 percent of registered voters said Bill Clinton’s presidency made them more likely to support Hillary, versus 16 percent who said it made them less likely. She also gets a gender boost: Twenty-four percent said they were more likely to support her because she’d be the first female president, while 11 percent said they’d be less likely to support her.

The other “dynasty presidencies” in American history – those of the Harrisons and the Roosevelts – also present a mixed picture of how the family dynamic can affect a campaign.

William Henry Harrison, the ninth president, served for only one month, in 1841. (He fell ill and died after delivering the longest inaugural address in US history.) But his legacy still hung over his grandson, Benjamin Harrison, when he ran for president in 1888. Puck cartoonist Joseph Keppler invented “Grandpa’s Hat” to ridicule the younger Harrison.

“Ben, a man of modest stature, was depicted each week as lost under a gigantic hat,” writes Brookings Institution scholar Stephen Hess in a 2009 op-ed in The Washington Post on political dynasties. Harrison won the election, but the cartoons continued. “The longer he was president, the more buried in the hat; by 1892 he had disappeared altogether, with Uncle Sam asking, ‘Where is he?’ ”

Harrison failed to win reelection.

The Roosevelts present a happier family tale, and a bipartisan one. Theodore, a Republican (president from 1901 to 1909) and Franklin, a Democrat (president from 1933 to 1945) were only fifth cousins, though bound tightly by Franklin’s marriage to Teddy’s niece Eleanor and by their exceptional political skills.

Franklin deeply admired his older cousin. “It was Theodore Roosevelt’s passionate idealism and principled leadership of 1907-1908 that was crucial in turning Franklin away from high society and toward grassroots politics at a critical period of the young law clerk’s life,” write James MacGregor Burns and Susan Dunn in their book “The Three Roosevelts.”

The Roosevelts’ career paths had striking parallels. Both served as assistant secretary of the Navy and governor of New York, and not by coincidence.

“In terms of Franklin Roosevelt’s career, putting him in a position to run for president, Teddy absolutely was essential,” says Thomas Whalen, a historian at Boston University. When Franklin first ran for president in 1932, “there was a feeling of nostalgia for Teddy.”

Most dynasties fade over time. On Mr. Hess’s top 10 list (see story, page 30), only three families – the Kennedys, the Bushes, and the Frelinghuysens – still have members in elective office: Rep. Joseph Kennedy III (D) of Massachusetts, state Sen. Edward Kennedy Jr. (D) of Connecticut, Republican Texas Land Commissioner George P. Bush, and Rep. Rodney Frelinghuysen (R) of New Jersey.

The Bushes and the Kennedys represent two models of dynasty-building.

“You’ve got the WASPy, blue-blood, Roosevelt-Bush model, which I would call ‘noblesse oblige,’ ” Ms. Perry says. “Then you have the immigrant, striving, up-from-the-peat-bogs-of-Ireland model of the Kennedys.”

In the Bush model, epitomized by the first President Bush, the culture was not to call attention to oneself – thus, his clipped syntax that avoids the word “I.”

“The Catholic Kennedys were shunned and ostracized by Boston Brahmins,” says Perry. “These were two very different societies and cultures and religions and family roots. The Kennedys called attention to themselves.”

Today, the “showiness” of the Kennedys is gone; they are as much an “old money” family as the Bushes. The Bush dynasty is changing, too. Jeb Bush is a Roman Catholic convert, and his wife is from Mexico. Their children, including politician son George P. Bush, are half Latino, emblematic of America’s growing diversity.

That the Kennedys and Bushes are still in politics is the exception: For every political scion who succeeds politically, there are dozens who don’t. Some get only so far and then wash out. F.D.R. Jr. served three terms in the House before a failed campaign for governor of New York. Another F.D.R. son, James, served five terms in the House before losing a nomination for mayor of Los Angeles.

Hess suggests this rule: “Voters give the children of important dynasts one free pass, a step up the political ladder before they must prove themselves.”

Hess also observes that the way to build a political dynasty is to have lots of children. In the past, that meant having lots of boys – and keeping the wild side in check, or at least out of public view.

“If you look at the Kennedys, the Bushes, and F.D.R.’s sons, all had playboy elements,” says Perry. “When they were young and irresponsible they were young and irresponsible. Some overcome that, like George W. and J.F.K. and Teddy [Kennedy], and some do not.”

Today, the rise of political daughters expands dynastic potential. In the 2014 midterms, several big-name “daughters of” ran and failed to win seats for the Democrats. (One exception is newly elected Rep. Gwen Graham (D) of Florida, daughter of a former governor and senator.) But it can be argued that the women who lost at least kept the races competitive, in part because of their famous last names, such as now-former Sen. Mary Landrieu (D) of Louisiana and Michelle Nunn, a Democrat who ran for the Senate from Georgia.

Clinton’s start as a political wife is, in a way, a throwback to the era when the only way a woman could get ahead in politics was through her husband. But Clinton’s active participation in her husband’s presidency and eight years as a senator made her a formidable (though unsuccessful) presidential candidate in 2008. Now, with her four years as secretary of State, Clinton has added to her résumé, but also has more to answer for in her expected second try at the presidency.

Clinton can expect to benefit from her husband’s strong economic record. But she can also expect another rehash of the scandals and intrigues of her husband’s presidency – many of which involved her, from Whitewater and the White House travel office controversy to President Clinton’s affair with Monica Lewinsky. Some critics of Hillary judge her harshly for staying with her husband.

All presidential candidates are called upon to answer for their past. But when your father and brother are ex-presidents, their pasts are also relevant. In Jeb Bush’s case, crucial decisions from his brother’s presidency – starting with a war in Iraq based on faulty intelligence – have quickly become Exhibit A. In a Feb. 18 speech to the Chicago Council on Global Affairs, he almost pleaded for mercy.

“Look, just for the record, one more time, I love my brother, I love my dad, I actually love my mother as well. Hope that’s OK,” Bush said to laughter. “And I admire their service to the nation and the difficult decisions that they had to make, but I’m my own man, and my views are shaped by my own thinking and my own experiences.”

Later, in response to a question, Bush allowed that “there were mistakes made in Iraq, for sure.” Bush has also said he doesn’t want to “re-litigate the past,” but the questions have only started – especially as instability throughout the Middle East remains a live issue.

• • •

Family matriarch Barbara Bush used to think that “more than two or three families” should run for high office. Now the former first lady is all for another Bush presidency.

Last April, most Americans – 69 percent – agreed with her original view, according to an NBC News/Wall Street Journal survey. And of those, most said their opinion applied equally to Hillary Clinton and Jeb Bush.

Another Bush presidency would be unprecedented – he would be the third from one family, and the only presidential brother to reach the Oval Office. A Hillary Clinton presidency would also be without parallel, as she would be the first woman in the job and the first to succeed a spouse.

Not that either candidate has a guarantee. Eight years ago, Clinton seemed headed for the Democratic nomination and the presidency. The big money was rolling in and she had the nation’s savviest political practitioner, Bill Clinton, at her side. Then Barack Obama happened.

Today, there appears to be no Obama on the horizon (as long as Sen. Elizabeth Warren (D) of Massachusetts stays out), and Clinton seems as sure a thing as any for either party, at least this far out. Bush is another matter. He ran his last campaign, reelection to the Florida governorship, 13 years ago. To most Americans, he is a blank slate. Bush could raise all the money in the world, but if he doesn’t impress primary and caucus voters, it will be for naught.

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Americans could just say, “Enough!” The prospective Republican field is full of fresh faces, starting with Gov. Scott Walker of Wisconsin, Sen. Marco Rubio of Florida, and Sen. Rand Paul of Kentucky, himself from a political family (though of a maverick sort).

Despite a history of voting for dynastic candidates, Americans “could reach a tipping point when you have one Bush too many or one Clinton too many or one Kennedy too many,” says Perry, the University of Virginia historian. “But these families are very skilled at how they perpetuate themselves. They continue to polish their images.” ρ