The Democrats who want to be president can't quite figure out how to talk about the most popular figure in their party. Former President Barack Obama still casts a long shadow over the 2020 primary campaign: Preserving Obama's legacy is the heart of former Vice President Joe Biden's pitch to voters — which has allowed his rivals to mark him as complacent. More left-leaning candidates, like Massachusetts Sen. Elizabeth Warren, say the next president needs to do more to push for health care reforms and combat income inequality — but lately, she's struggling to sell her proposals. Former Obama Cabinet Secretary Julián Castro has ripped his ex-boss' record on immigration and deportation. South Bend, Indiana, Mayor Pete Buttigieg raced to have a reporter correct a story that misquoted him citing "failures of the Obama era." Picking and choosing which parts of Obama's tenure to embrace, and how much, has become a delicate game in the primary season.

And now Obama himself is working to cool down what he sees as an overheated political climate. In October, at a panel discussion for his foundation, he warned against the pitfalls of "woke" online cancel culture, telling a gathering of young activists that "if all you're doing is casting stones, you're probably not going to get that far." This month, at a gathering of influential Democrats, he cautioned the 2020 contenders against pushing too far, too fast on policy: "This is still a country that is less revolutionary than it is interested in improvement."

That distinction helps explain why so many of the candidates' proposals seem so far to the left of Obama. The former president was skeptical of sweeping change, bullish on markets, sanguine about the use of military force, high on individual responsibility and faithful to a set of old-school personal values. Compare that with the agenda of his would-be successors: Medicare for All, free college, a wealth tax, universal basic income.

Given the political climate, it's no surprise to see the party's base clamoring for something more dramatic. But the contrast between Obama's steady approach and the seeming radicalism of his Democratic heirs can't simply be chalked up to changing times. It's because the former president, going back at least to his 2004 Senate race, hasn't really occupied the left side of the ideological political spectrum. He wasn't a Republican, obviously: He never professed a desire to starve the federal government, and he opposed the Iraq war that Republicans overwhelmingly supported. But to the dismay of many on the left, and the continuing disbelief of many on the right, Obama never dramatically departed from the approach of presidents who came before him.

There's a simple reason for that: Barack Obama is a conservative.

No, he isn't a Republican. He never professed a desire to starve the federal government, and he opposed the Iraq war that Republicans overwhelmingly supported. But he was, and remains, skeptical of sweeping change, bullish on markets, sanguine about the use of military force, high on individual responsibility and faithful to a set of old-school personal values. To the dismay of many on the left, and to the continuing disbelief of many on the right, Obama never dramatically departed from the approach of presidents who came before him.

Obama's perspectives don't line up with every position now seen as right-of-center: He joined the Paris climate accords, he signed Dodd-Frank financial-sector regulation and he's pro-choice. But even on that issue, in one of the first times he outlined his stance on abortion to a national constituency, Obama explained that as the father of daughters, "if they make a mistake, I don't want them punished with a baby" — a framing that outraged anti-choice advocates, but also hinted at a patriarchal sensibility. He flip-flopped to supporting same-sex marriage, but with an emphasis on marriage.

His constant search for consensus, for ways to bring Blue America and Red America together, could lead him to policies that used Republican means to achieve more liberal ends.

The underlying concept for Obama's signature legislation, the Affordable Care Act, with its individual mandate, was devised by the right-wing Heritage Foundation and was first implemented at the state level by Sen. Mitt Romney, R-Utah, then governor of Massachusetts. Obama wanted to protect Americans from the catastrophic effects of a prolonged recession, so he agreed, in his last meaningful vote as a senator, to a bailout of banks — and, as president, prioritized recovery over punishing banks and bankers for their role in the financial crisis. Until the Sandy Hook tragedy in 2012, Obama studiously avoided any push for gun control. Indeed, in 2010, he signed laws that loosened restrictions on bringing firearms to national parks and on Amtrak. Though cast as a "dithering" peacenik, he stuck with his thesis that the imperative "to end the war in Iraq is to be able to get more troops into Afghanistan" and prosecuted a drone war in Pakistan, Afghanistan and Yemen.

But Obama's approach to politics was marked by a circumspection that went even deeper than policies. As he recently said, "the average American doesn't think that we have to completely tear down the system and remake it." To be conservative, as philosopher-guru Michael Oakeshott, a conservative hero, once put it, "is to prefer the familiar to the unknown, to prefer the tried to the untried, fact to mystery, the actual to the possible, the limited to the unbounded, the near to the distant, the sufficient to the superabundant, the convenient to the perfect, present laughter to utopian bliss."

Obama believes, fundamentally, that the American model works — but, crucially, that it hasn't been allowed to work for everyone. He believes that in some cases, it's the government's role to help expand the American dream to individuals and communities to whom that dream has been denied. And in others, he believes Americans can achieve the dream if only they show the will to surmount obstacles on their own.

His second inaugural address was a thoroughly conservative document, underscoring equality of opportunity, as opposed to equality of outcome. Republican former House speaker Newt Gingrich's reaction at the time was: "95 percent of the speech I thought was classically American, emphasizing hard work, emphasizing self-reliance, emphasizing doing things together."

In his first year in office, he gave a back-to-school address that Republicans panned in advance as big-brotherism, even its though its central idea turned out to be: "At the end of the day, the circumstances of your life — what you look like, where you come from, how much money you have, what you've got going on at home — none of that is an excuse for neglecting your homework or having a bad attitude in school."

He once argued that in certain circumstances, government programs created welfare dependency, saying that "as somebody who worked in low-income neighborhoods, I've seen it where people weren't encouraged to work, weren't encouraged to upgrade their skills, were just getting a check, and over time their motivation started to diminish."

In remarks commemorating the 50th anniversary of the March on Washington, Obama went out of his way to lecture that, in the civil rights era, "what had once been a call for equality of opportunity, the chance for all Americans to work hard and get ahead, was too often framed as a mere desire for government support, as if we had no agency in our own liberation, as if poverty was an excuse for not raising your child, and the bigotry of others was reason to give up on yourself." You'd never hear that sentiment expressed by Sen. Bernie Sanders, I-Vt., for whom structural inequality explains nearly every American ill.

He was unapologetic about his identity as a role model for black men, in particular, and his grounding in African-American intellectual and political traditions. And he repeatedly stressed that not all inequities in American society are attributable to discrimination, racial or otherwise. Striking that balance was precisely what granted Obama currency with the black electorate, which votes overwhelmingly for Democrats and is the core of the party's base, but frequently skews moderate to conservative, ideologically.

He embraced respectability politics as a way to communicate the sameness of a first family of color: The many Norman Rockwell-worthy photo-ops — the Obamas' 2009 family portrait, done by Annie Leibovitz, a study in wholesome family living; their annual vacations on Martha's Vineyard, summer haven of the black elite; dialing back his storied "cool," as when he displayed his stiff dance moves during an appearance "Ellen," laying claim to the mantle of the everyman dad. When asked what he thought about Kanye West interrupting Taylor Swift's 2009 MTV Video Music Awards acceptance speech to shower praise on Beyoncé, Obama offered no mitigating analysis, saying simply, "He's a jackass."

In his 2014 immigration reform speech, he leaned on Exodus 23:9.

Obama called out racism in the criminal justice system. He met with Black Lives Matter activists, and his Justice Department used consent decrees to rein in police departments. For this, he was often portrayed as a cop-hater in right-wing media; former Milwaukee County Sheriff David Clarke, a Fox News fixture, called him "the most anti-cop president I have ever seen." But the president routinely extolled law enforcement, including at the 2015 convention of the International Association of Chiefs of Police, when he said: "I reject any narrative that seeks to divide police and communities that they serve. I reject a story line that says when it comes to public safety there's an 'us' and a 'them.' "

After George Zimmerman's acquittal, Obama — who had said "Trayvon Martin could have been me 35 years ago" — defended the system, emphasizing that "we are a nation of laws and a jury has spoken."

For most of his presidency, Obama governed with a Republican Congress dedicated to preventing his re-election or thwarting his agenda. Any efforts would have to entail compromise. Still, he made bargains that the rhetoric of current Democratic candidates would seem to foreclose. In 2010, Obama and Republicans traded a two-year extension of former President George W. Bush's top marginal income tax cut, along with a payroll tax holiday and an extension of unemployment benefits, that paved the way for a repeal of Don't Ask, Don't Tell. At the time the left fumed, but in that deal Obama benefited from both the quid and the quo. He later also agreed to the Budget Control Act of 2011, known as "sequestration," that brought down year-to-year deficits by slashing federal spending in exchange for GOP votes to raise the debt ceiling.

Obama was a believer in big government, but his views show many similarities with to those of Republican presidents like Theodore Roosevelt, who fought corporate monopolies and later led the Progressive Party; Dwight D. Eisenhower, who signed the Civil Rights Act of 1957 and the Federal Aid Highway Act, creating the interstate highway system; and establishment archetype George H.W. Bush, a veteran of Congress, the U.N., the CIA and the vice presidency who broke his "no new taxes" pledge, rescued savings and loans and declared an import ban on semi-automatic rifles. His conservatism also lines up with the late senator Edward Brooke, R-Mass., a cosponsor of the Fair Housing Act of 1968 who was the last black man to serve in the Senate before Obama.

Obama did advance priorities that progressives cheered: He tripled the number of women on the Supreme Court. On the environment, he implemented aggressive rules to limit coal-based power and ozone and mercury emissions. He supported anti-discrimination laws for LGBT employees and introduced rules that would protect some younger, undocumented immigrants from deportation. (He achieved many of these policies through executive fiat, meaning they are — or have already been — easily reversed.) But none of these changes revolutionized governance or structurally reordered American life.

The scramble that Obama can still cause reflects the dissonance he's generated for a decade: The center-left adores him, but to the far left he's a sellout. He's being rethought on the center-right, but remains the bête noire of the far right, which morphed from the (putatively) government-hating Tea Party wing to a strong-man-loving Republican core.

That's due, in part, to an enduring misunderstanding of what he represented.

Notwithstanding the change-we-can-believe-in marketing that propelled his political rise, Obama's aim was never to turn things upside down. Favoring "the familiar to the unknown" was Obama's disposition, but also his project: Expanding a traditional slate of priorities — the familiar American dream, not a reconceived one — to Americans for whom it had been previously denied. Part of that project was building, gradually, at moments almost reverently, on his predecessors' foundation.

That's left Republicans lurching in President Trump's direction. And forces Democrats to sort out who they are; and how to fuse Obama's appeal with an agenda that reaches further than he ever tried — or saw the need to.

David Swerdlick is an assistant editor for the Washington Post's Outlook section and PostEverything blog.