President Biden was peeved. What was Chuck Schumer thinking?

The Democrats had just temporarily averted a national default with Republican aid but still needed a broader deal to resolve a debt ceiling clash. Yet there was Mr. Schumer, the Senate Democratic leader, on the floor bashing Republicans for playing “a dangerous and risky partisan game.”

Mr. Biden called Mr. Schumer to chide him. That was not helpful, the president said, according to an official informed about the call late in his first year in office. Senator Mitch McConnell, the Republican leader, had backed down to help avoid a fiscal crisis. They should not rub his nose in it. Mr. Schumer pushed back. “You don’t know how much he’s been beating up on me,” he told the president.

The Joe Biden who will defend his presidency at a nationally televised debate on Thursday night remains a practitioner of old-school politics in a new-school era. The hostility, the anger, the polarization, the “beating up” that define today’s national debate, yes, he knows all about that. But after more than half a century in Washington, he still has the instincts of a backslapping cloakroom pol, eager to make deals and work across the aisle where possible at a time when that rarely seems rewarded anymore.

In some ways, it has been a formula for success that upended expectations, resulting in a raft of landmark liberal programs that will mark Mr. Biden in the history books as one of the most prolific legislative masters since Lyndon B. Johnson. And yet it has not been a formula for executing the most essential mission that he assigned himself when he took office: healing a broken country riven by profound economic, ideological, cultural, political and geographic divisions.

No president in American history took the oath with more experience in public office than Mr. Biden, 81, who was first elected to the Senate in 1972, when two-thirds of today’s Americans were not even born. But the politics of 2024 are a far cry from those of the 1970s, 1980s, 1990s, 2000s or even 2010s. While building a new bridge or lowering the cost of insulin still matter, they only penetrate so far with the electorate in an era of tribal animosity, populist unrest and social media disinformation.

“These days, people like to belittle experience, but his experience was just vital to getting as much done as we did,” Mr. Schumer said in an interview. Although he said he did not recall the 2021 phone call with Mr. Biden, he did not deny it either, and agreed that it sounded like the president’s approach. “Biden was always of the view and understood instinctively that we had to do things in a bipartisan way,” Mr. Schumer said, adding that he concurred.