Early polls showing Joseph Biden leading the large field of Democrats who are potential candidates for president in 2020 may leave some wondering what the Democrats could possibly be thinking.

Against President Trump, the Democrats would match up their own East Coast white male candidate in his 70s who doesn’t drink alcohol and didn’t serve in Vietnam? It would seem to violate Phyllis Schlafly’s “choice not an echo” theory of how American presidents are chosen.

The polls, though, are picking up a truth perhaps not immediately obvious to casual observers, which is that a strong case can be made for Biden as the Democratic nominee in 2020. He’s something unusual in presidential politics: a candidate who can excite the party’s base while also winning back independents and voters in swing states and swing districts — the voters and places that supported Mr. Obama in 2012 but Mr. Trump in 2016.

The “excite the base” part has to do with Mr. Biden’s eight-year tenure as the loyal, steady vice president to Barack Obama, a president who remains a highly popular and influential figure among Democrats. You name the Obama “achievement” — the stimulus, ObamaCare, the Iran nuclear deal — and Mr. Biden was right there in the center of the action. Mr. Biden also expressed public support in May 2012 for same-sex marriage, even before President Obama did.

The crossover appeal part has to do with the ability of Mr. Biden, as the son of a used-car salesman from Scranton, Pennsylvania, to connect with blue-collar Middle American voters, Reagan Democrats, and suburban Catholics. Back in July 2008, when Mr. Biden’s name first surfaced as a potential running mate for Obama, a New York Sun editorial mentioned at least four votes by Biden to outlaw a procedure known as partial-birth abortion. Mr. Biden was one of 17 Senate Democrats who backed legislation signed into law by President George W. Bush outlawing partial-birth abortion.

Nor is abortion the only area in which Mr. Biden might be willing to deviate from the progressive party line. Though he has strong and longstanding ties to organized labor, as a senator he voted for the North American Free Trade Agreement. While he opposed the Gulf War during the George H.W. Bush administration, his instincts on foreign policy tend more internationalist, even interventionist, than hard-left. He was a hawk on Bosnia.

As a young reporter in Washington more than two decades ago I once watched Mr. Biden sit around a table in a Senate office building with a dozen advocates of democracy promotion, and it’s impossible to forget what seemed like Mr. Biden’s genuine enthusiasm for and dedication to the idea of spreading American-style freedom and rule of law worldwide.

Two other factors weigh in Mr. Biden’s favor. He hires well. Chief of staff to the vice president is one of the most underrated but quietly influential jobs in Washington. William Kristol did that job for Dan Quayle, and Scooter Libby served Dick Cheney. Mr. Biden’s chiefs of staff were Ron Klain, Bruce Reed, and Steve Ricchetti, three veterans of the Clinton administration.

Mr. Reed, a Rhodes scholar, is known as a centrist, New Democrat type who helped President Clinton reform welfare. Mr. Klain, who clerked for Supreme Court Justice Byron White, is a classic Washington mentor-connector who heroically helped prevent the Ebola virus from spreading to the United States.

Mr. Biden’s got good interpersonal negotiating skills, in part as a result of his insight that you can get more done if you avoid questioning people’s motives. Mr. Biden’s working relationship with Jesse Helms, the Republican Senator from North Carolina who was a senior figure on the Senate Foreign Relations Committee, was the subject of a classic and memorable speech Mr. Biden gave in May 2015 at Yale University’s Class Day.

Said Biden: “When you question a man’s motive, when you say they’re acting out of greed, they’re in the pocket of an interest group, et cetera, it’s awful hard to reach consensus. It’s awful hard having to reach across the table and shake hands. No matter how bitterly you disagree, though, it is always possible if you question judgment and not motive.”

Whether the Democrats are ready for that message in 2020, or in 2019, is a question that, if Mr. Biden does enter the race, primary voters and caucus-goers will have a chance to decide. As for whether the country as a whole could benefit from it — well, this isn’t an endorsement column. It’s not too soon at all, though, to say we could do plenty worse.