Each of them has sat behind the Resolute Desk in the Oval Office, signed bills into law, appointed judges, bartered with foreign leaders and ordered the armed forces into combat. They both know what it is like to be the most powerful person on the planet.

Yet the general election matchup that seems likely after this week’s New Hampshire primary represents more than the first-in-a-century contest between two men who have both lived in the White House. It represents the clash of two presidents of profoundly different countries, the president of Blue America versus the president of Red America.

The looming showdown between President Biden and former President Donald J. Trump, assuming Nikki Haley cannot pull off a hail-mary surprise, goes beyond the binary liberal-conservative split of two political parties familiar to generations of Americans. It is at least partly about ideology, yes, but also fundamentally about race and religion and culture and economics and democracy and retribution and most of all, perhaps, about identity.

It is about two vastly disparate visions of America led by two presidents who, other than their age and the most recent entry on their résumés, could hardly be more dissimilar. Mr. Biden leads an America that, as he sees it, embraces diversity, democratic institutions and traditional norms, that considers government at its best to be a force for good in society. Mr. Trump leads an America where, in his view, the system has been corrupted by dark conspiracies and the undeserving are favored over hard-working everyday people.

Deep divisions in the United States are not new; indeed, they can be traced back to the Constitutional Convention and the days of John Adams versus Thomas Jefferson. But according to some scholars, they have rarely reached the levels seen today, when Red and Blue Americas are moving farther and farther apart geographically, philosophically, financially, educationally and informationally.

Americans do not just disagree with each other, they live in different realities, each with its own self-reinforcing Internet-and-media ecosphere. The Jan. 6, 2021, attack on the Capitol was either an outrageous insurrection in service of an unconstitutional power grab by a proto-fascist or a legitimate protest that may have gotten out of hand but has been exploited by the other side and turned patriots into hostages.

The two lands have radically different laws on access to abortion and guns. The partisan breakdown is so cemented in 44 states that they effectively already sit in one America or the other when it comes to the fall election. That means they will barely see one of the candidates, who will focus mainly on six battleground states that will decide the presidency.

In an increasingly tribal society, Americans describe their differences more personally. Since Mr. Trump’s election in 2016, according to the Pew Research Center, the share of Democrats who see Republicans as immoral has grown from 35 percent to 63 percent while 72 percent of Republicans say the same about Democrats, up from 47 percent. In 1960, about 4 percent of Americans said they would be displeased if their child married someone from the other party. By 2020, that had grown to nearly four in 10. Indeed, only about 4 percent of all marriages today are between a Republican and a Democrat.

“Today, when we think about America, we make the essential error of imagining it as a single nation, a marbled mix of red and blue people,” Michael Podhorzer, a former political director of the AFL-CIO, wrote in an essay last month. “But America has never been one nation. We are a federated republic of two nations: Red Nation and Blue Nation. This is not a metaphor; it is a geographic and historical reality.”

The current divide reflects the most significant political realignment since Republicans captured the South and Democrats the North following the civil rights legislation of the 1960s. Mr. Trump has transformed the G.O.P. into the party of the white working class, rooted strongly in rural communities and resentful of globalization, while Mr. Biden’s Democrats have increasingly become the party of the more highly educated and economically better off, who have thrived in the information age.

“Trump was not the cause of this realignment, since it has been building since the early 1990s,” said Douglas B. Sosnik, who was a White House counselor to President Bill Clinton and studies political trends. But “his victory in 2016 and his presidency accelerated these trends. And this realignment is largely based on the winners and losers in the new 21st-century digital economy, and the best predictor of whether you are a winner or loser is your level of education.”

The leaders of these two Americas each wield power in their own way. As the current occupant of the White House, Mr. Biden has all the advantages and disadvantages of incumbency. But Mr. Trump has been acting as an incumbent in a fashion too — he never conceded his 2020 defeat and the majority of his supporters, polls show, believe that he, not Mr. Biden, is the legitimate president.

Even without a formal office, Mr. Trump has set the agenda for Republicans in Washington and the state capitals. He encouraged the internal coup that took down Speaker Kevin McCarthy last year after he made a spending deal with Mr. Biden. He is advising the current speaker, Mike Johnson, on how to handle the impasse over border policy and security aid for Ukraine.

Many elected Republicans who once stood against Mr. Trump, with notable exceptions, have rushed to endorse him in recent weeks as his claim to the party’s presidential nomination has grown almost complete. As a result, it is hard to imagine any major policy deal coming together in Washington this year without Mr. Trump’s approval or at least his acquiescence.

The current situation has no exact analog in American history. Only twice before have two presidents faced off against each other. In 1892, former President Grover Cleveland won a rematch against President Benjamin Harrison. In 1912, former President Theodore Roosevelt lost a third-party bid to depose his successor and estranged protégé, President William Howard Taft, but paved the way for victory by the Democratic candidate, Woodrow Wilson.

Neither of those contests reflected the kind of epochal moment that scholars and political professionals see this year. When historians search for parallels, they often point to the period before the Civil War, when an industrializing North and an agrarian South were divided over slavery. While secession today is far-fetched, the fact that it nonetheless comes up in conversation among Democrats in California and Republicans in Texas from time to time indicates how divorced many Americans feel from each other.

“Whenever I mention the 1850s, everyone thinks we are going to have a civil war,” said Sean Wilentz, a Princeton historian who was among a group of scholars who met recently with Mr. Biden. “I’m not saying that. It’s not predictive. But when institutions are weakened or changed or transformed the way they have, you can get perspective from history. I think people have yet to understand just how abnormal the situation is.”

Mr. Biden and Mr. Trump are both historically unpopular presidents. Mr. Biden opens his re-election year with an approval rating of just 39 percent in Gallup polling, the lowest of any elected president at this point going back to Dwight D. Eisenhower. The two are essentially equal in favorability, a slightly different question, with 41 percent expressing positive feelings about Mr. Biden compared with 42 percent about Mr. Trump.

But they represent different electorates. Mr. Biden is viewed favorably by 82 percent of Democrats but only 4 percent of Republicans. Mr. Trump is viewed favorably by 79 percent of Republicans but only 6 percent of Democrats.

In Mr. Sosnik’s latest analysis, Mr. Biden starts the general election with 226 likely votes in the Electoral College and Mr. Trump with 235. To get to the 270 needed for victory, one of them will have to harvest some of the 77 votes up for grab in half a dozen states: Arizona, Georgia, Michigan, Nevada, Pennsylvania and Wisconsin.

Because Mr. Biden and Mr. Trump have both served as president, Americans already know what they think about them. That will make it harder for either to define his opponent with the public the way that President George W. Bush defined John F. Kerry in 2004 and President Barack Obama defined Mitt Romney in 2012.

But the wild cards this year remain unique nonetheless — an 81-year-old incumbent who is already the oldest president in American history against a 77-year-old predecessor who is facing 91 felony counts in four separate criminal indictments. No one can say for sure how those dynamics will play out over the next 285 days, which Mr. Biden and Mr. Trump are already treating as the general election presidential campaign.

And while voters may already have some sense of how the winner will operate in the White House over the next four years, it is not at all clear how a divided country will respond to victory by one or the other. Rejectionism, disruption, further schism, even violence all seem possible.

As Mr. Wilentz said, “Things are not normal here. I think that’s important for people to understand.”

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