Well before Election Day in 2004, President George W. Bush was warned by strategists that he would face a tough campaign battle because of voter distress over the war in Iraq and over the economy — two issues he had once hoped to ride to a second term.

Mr. Bush’s aides moved quickly to retool the campaign. They turned attention away from the president and his record and set out to portray his likely Democratic opponent, Senator John Kerry of Massachusetts, a Vietnam War veteran, as a flip-flopper, unreliable on national security and unfit to lead a nation still reeling from the terror attacks of Sept. 11.

“We saw a weakness we knew we could exploit to our advantage in what was going to be a close election,” said Karl Rove, Mr. Bush’s longtime senior political adviser.

Eight years later, aides to another sitting president, Barack Obama, reviewing public and private polls, concluded that concern among voters about the lingering effects of the Great Recession and the direction of the nation could derail his hopes for a second term.

Taking a lesson from Mr. Bush, Mr. Obama recast his campaign away from his first-term record and set out to discredit his opponent, Mitt Romney, the former governor of Massachusetts, as a wealthy businessman unsympathetic to working-class Americans.

President Biden is hardly the first president during this era of division and polarization to be confronted with polling data suggesting his re-election was at risk. But the re-election campaigns rolled out by Mr. Bush and Mr. Obama, who both returned to second terms in the White House, stand today as reminders that polls this early are not predictions of what will happen on Election Day. In the hands of a nimble candidate, they can even be a road map for turning around a struggling campaign.

Mr. Bush and Mr. Obama were different candidates facing different obstacles: a quagmire of a war for Mr. Bush, a domestic economy shaken by the global financial crisis of 2008 for Mr. Obama. But both moved to transform their re-election campaigns from a referendum on the incumbent into a contrast with an opponent they defined, with slashing television advertisements, months before either Mr. Romney or Mr. Kerry were nominated at their party conventions.

By contrast, a modern-day Republican president who lost a bid for a second term, George H.W. Bush in 1992, failed to heed polls showing voters distressed about the economy and ready for a change after 12 years of Republicans in the White House.

The elder Mr. Bush, his aides said in recent interviews, was lulled by the accolades for leading the coalition that repelled Saddam Hussein and Iraq out of Kuwait, and contempt for his opponent, a young Democratic governor who had avoided the draft and had a history of extramarital liaisons.

“Biden has a very high degree of difficulty but I think the race is winnable,” said David Plouffe, who was a senior adviser to Mr. Obama’s re-election campaign. “Listen, I have sympathy for an incumbent president or governor who says, ‘people need to know more about my accomplishments.’ That is true, but at the end of the day this is a comparative exercise. That’s the one thing we learned.”

The Biden White House has dismissed polls — including a New York Times/Siena College poll released last week — as meaningless this far before Election Day. The president’s advisers pointed to Democratic gains in this month’s elections as evidence that the party and its standard-bearer are in fine shape.

Yet, after months of trying to run on his economic record with little sign of success, Mr. Biden has begun turning his attention more to Donald J. Trump, the Republican former president and his likely opponent, particularly his policies on immigration and abortion rights. That includes an advertisement that shows Mr. Trump plodding through a golf course as the announcer said that Mr. Trump pushed through tax cuts “for his rich friends” while U.S. automakers shut down plants.

“We are absolutely looking at ways that we can help drive the conversation around Trump and MAGA as much as we can,” said Kevin Munoz, the Biden campaign spokesman. But, Mr. Munoz added, “We are in a different position than Obama and Bush. We had very strong midterms. We have had very strong special elections. Our theory of the case was proved again last Tuesday.”

Upending the race dynamics might prove more daunting for Mr. Biden than for his predecessors. Mr. Obama and George W. Bush were able to discredit Mr. Romney and Mr. Kerry because voters, at this early stage of the general election campaign, did not know much about them.

But there is not much the Biden campaign can tell voters about Mr. Trump that they don’t already know. (Or for that matter, not much Mr. Biden can tell voters about Mr. Biden that they don’t already know.) And Mr. Trump has, so far at least, not paid a political cost for the kind of statements — such as when he described his critics as “vermin” — that might have previously derailed a more conventional candidate. Being indicted on 91 criminal counts in four cases has, so far, only solidified his support.

When Mr. Bush’s campaign began planning for his re-election, they confronted polling numbers that — while not as unnerving for the president as some that have come out in recent weeks about Mr. Biden — were cause for concern. A poll by the Pew Research Group found that 46 percent of respondents said Mr. Bush’s economic policies had made the economy worse and 39 percent said American troops should be brought back from Iraq as soon as possible; up from 32 percent the month before.

“We decided early on that we wanted to make the election about national security even though the economy was the No. 1 issue,” said Matthew Dowd, the chief strategist for Mr. Bush’s 2004 campaign. “We were at a disadvantage to Dems on the economy. And as part of that strategy, we desired to define Kerry negatively on national security early on, and as a weak flip-flopping leader so we could position Bush as a strong leader and strong on national security.”

Before long, the Bush campaign was on the air with advertisements assailing Mr. Kerry for pledging to roll back the Patriot Act, giving the federal government expanded powers to go after terrorists. The Patriot Act was passed shortly after the Sept. 11 attacks with overwhelming support in Congress — including Mr. Kerry.

“John Kerry. Playing politics with national security,” an announcer said.

Eight years later, as Mr. Obama mounted his re-election campaign, many Americans were telling pollsters that the country was heading in the wrong direction and that they were worse off financially than they had been before Mr. Obama took office. For instance, a Washington Post/ABC News poll found three-quarters of Americans saying the country was heading in the wrong direction.

Mr. Obama’s advisers studied the re-election campaigns of other embattled sitting presidents. “We knew that most re-elect campaigns were a referendum,” said Joel Benenson, who was the pollster for Mr. Obama’s team. “We also knew we had this massive economic crisis which absolutely was not all of Obama’s making. But we also knew you are the incumbent president, and you can’t blame it on your predecessor. We couldn’t convince them that the economy was getting better.”

But Mr. Romney, he said, “was not fully formed with voters,” which was an opportunity to spotlight his wealth and portray him as someone whose policies would favor the rich.

By contrast, George H.W. Bush, aides said, disregarded the warnings, confident the near 90 percent voter approval rating he registered after the war in Kuwait made his re-election all but certain. “The adulation from the war somehow muted the normal political instincts of a lot of people around the president,” said Ron Kaufman, who was a senior adviser to that campaign.

Mr. Rove said Mr. Biden was in worse shape today than the elder Mr. Bush had been in 1992. “Bush seemed bereft of ideas for the future, but people saw him as an admirable human being,” Mr. Rove said. “The problem for Biden is that people have concluded he’s not up to the job — too old and lacking the necessary stamina and mental acuity.”

In recent polls conducted in five battleground states by The New York Times and Siena College, 71 percent of respondents said Mr. Biden was “too old” to be an effective president.

Mr. Plouffe said the Biden campaign should embrace the lesson the Obama campaign learned studying the losing campaign of the elder Mr. Bush. “The Bush people tried to convince people that the economy was better than they thought it was,” he said. “One thing I’ve learned is you can’t tell people what they think about the economy. They’ll tell you what they think about the economy.”

“I’d start every speech saying, ‘America is faced with a choice, we are both old white men,’” Mr. Plouffe said. “‘But that’s where the similarities end.’”