Because our nation’s creation is the result of revolting against a revolting king, we Americans are predisposed to being skeptical about political dynasties. True, we’ve elected some silver spoons, but still we’re leery of those who try to float along their famous gene pool, or those who dive in by marriage. Fundamentally, we suspect that they’ve received some unearned advantage. Fair or not, there’s been a lot of grumbling right now about the prospect of a White House race between still another Bush and still another Clinton.

Is lineage really such an advantage? Probably, that’s a resounding “yes” and “no.” Arguably, with all their qualifications, Jeb Bush and Hillary Clinton might not have risen to the heights of competing for the presidency were it not for accidents of birth or matrimony. Still, as they are painfully discovering, they carry some heavy family baggage.

In Jeb’s case, it is brother George W., the immediate ex-POTUS. It seems like wherever he turns, Jeb Bush is constantly confronted about brother George’s Iraq War, which is widely viewed as a huge mistake. Jeb sometimes has botched his response, but in fairness, he’s in an impossible situation where his choice is to appear disloyal to his brother or to support an unpopular military adventure. He couldn’t even go to the Iowa State Fair, which is supposed to be a jolly, hokey campaign ritual, without being hammered with uncomfortable questions about Iraq. It gets under his skin. “This is kind of a tough game for me to be playing, to be honest with you,” he said at the fair. “I’m my own person.” But this person owns a family legacy, whether he likes it or not. Chances are it’s both.

Meanwhile, Hillary Clinton has risen from her role of long-suffering “wife-of” and parlayed that into an opportunity to establish her own record as a senator and secretary of state and is now reaching for the highest star. But it’s the history of controversies during Bill Clinton’s time as chief executive that is making it really difficult to shake off the persistent charges so familiar from back in the day. Her responses to her recent email debacle, for example, resemble the grudging parsing of information that so characterized Clinton 1. Unfortunately for her, too many recall the tactics and are leery of them.

In both cases, Jeb Bush and Hillary Clinton have started out as favorites for their parties’ nomination, partly because of their names. But they’re both struggling. Bush is tumbling in the polls, and it goes beyond his being Trumped, along with all the other GOP candidates. More than any of the others, he would like to present himself as the established grown-up, but disgusted Americans are celebrating anti-establishment approaches to our problems, no matter how immature. Sensible is not the name of the game right now, and having an old, familiar name is a great big negative for those who are furious about the old and familiar.

Meanwhile, enthusiasm for Hillary is beginning to wane, to put it mildly, among Democrats who fret not just about her credibility problems but about her stiff and wooden campaigning. Things are so bad that among the names floated as possible alternatives is Al Gore — Mr. Stiff and Wooden himself. More importantly, Joe Biden is giving all the appearances that he is considering the race. The good news for Hillary is a Biden candidacy would certainly shatter a perception that she’s cakewalking through the election with a certain sense of entitlement. But that’s the only good news.

Biden is popular throughout the Democratic Party he has represented during his long career in politics. He’s considered warm, affable and spontaneous compared with the always-scripted Hillary. Plus, he doesn’t have to deal with the dynasty issue. He’s the one who built his. Hillary Clinton and Jeb Bush will now have to show that they’ve risen above theirs.

Bob Franken is a longtime broadcast journalist, including 20 years at CNN.