Since his death, Jimmy Carter has been lauded for brokering the Camp David Accords and for his post-White House mission to help the poor and battle disease. But glossed over amid all the tributes is the burdensome legacy that Mr. Carter left for his Democratic Party: a presidency long caricatured as a symbol of ineffectiveness and weakness.

This perception has shadowed the party for nearly 40 years. It was forged in the seizure of American hostages by Iranian militants in 1979 and the failed military attempt to free them, as well as the invasion of Afghanistan by the Soviet Union. And it lingered in memories of Mr. Carter wearing a cardigan as he asked Americans to conserve energy, or bemoaning what he called a “crisis of confidence” in an address to the nation that became a textbook example of political self-harm.

Over the decades, these events have provided endless fodder for attacks by Republicans, who reveled in invoking Mr. Carter’s name to deride Democrats. And that mockery, in turn, influenced the way Democrats have presented themselves to voters. Without Mr. Carter’s image of weakness on national security and defense, for example, it is hard to imagine the party’s war-hero candidate for president in 2004 introducing himself with a salute at its nominating convention and saying, “I’m John Kerry and I’m reporting for duty.”

Mr. Carter’s political legacy produced what many analysts argue was a kind of conditioned response: an overreaction among Democrats anxious to avoid comparisons to him on foreign policy issues. This was evident in the roster of prominent congressional Democrats, including Hillary Clinton, who voted for the 2002 resolution that authorized President George W. Bush to take the nation to war in Iraq, a vote many said they came to regret.

It could even be discerned in the taciturn response from President Biden after the U.S. withdrawal from Afghanistan in 2021 descended into chaos, said Julian E. Zelizer, a professor of political history at Princeton.

“Democrats always feel defensive about these messy situations,” Professor Zelizer said. He linked that reflex to the taking of the Iranian hostages and to the raid Mr. Carter ordered to save them, which ended in a helicopter crash that killed eight Americans.

“They don’t act with command in talking about tough foreign policy events,” Mr. Zelizer said, pointing in particular to the struggle by Democrats in Congress over Iraq. “The instinct when things go bad is to either be silent or apologetic.”

Historians and Democrats say the characterization of Mr. Carter as weak is in many ways unfair and exaggerated, ignoring some of the major accomplishments of his four years in office. He ordered an American boycott of the 1980 Summer Olympics in Moscow and a grain embargo against the Soviet Union after its invasion of Afghanistan.

Nonetheless, “He became an exemplar of why you had to look tough and not weak in foreign policy,” said Robert Shrum, a Democratic consultant who worked for Senator Edward M. Kennedy of Massachusetts when Mr. Kennedy challenged Mr. Carter for the presidential nomination in 1980.

Indeed, more than 30 years after Mr. Carter left office, Republicans reached back to the Carter years to dismiss a momentous decision by President Barack Obama that delivered a forceful rebuttal to the idea of Democrats as weak or ineffective: approving the American raid to assassinate Osama bin Laden in 2011.

“Even Jimmy Carter would have given that order,” said Mitt Romney, the Republican candidate for president.

(None other than Mr. Biden, as Mr. Obama’s vice president, made that raid a staple of his speeches in their 2012 re-election campaign. “Osama bin Laden is dead, and General Motors is alive,” Mr. Biden said often.)

This aspect of Mr. Carter’s legacy was ultimately set in cement by his defeat at the hands of Ronald Reagan, a former actor and governor who presented himself as a decisive and forceful contrast to the sitting president. “He was the standard by which Democrats and Republicans judged political effectiveness,” Tim Naftali, a presidential historian, said of Mr. Reagan. “So by definition, Carter, whom Reagan had beaten, was the opposite of effective, the model to be avoided.”

“The killer Reagan line, ‘Are you better off than you were four years ago?’ was first aimed at Carter,” he said.

So it was that from the moment Mr. Carter left office — on the day Iranian militants released the hostages — Democratic candidates for president have sought, with word and action, to escape his shadow.

Bill Clinton frequently invoked strength in talking about both international and domestic issues when he ran for president. During his 1996 re-election campaign, he boasted of putting 100,000 police on the street and promised to keep America “the world’s strongest force for peace and freedom and prosperity.”

For her part, Mrs. Clinton, who as the Democratic candidate in 2016 also had to allay voters’ doubts about whether a woman had the fortitude to be president, repeatedly cited her experience as secretary of state under Mr. Obama, and made “Stronger together” her campaign slogan. She used the words “strong,” “stronger” and “strength” 13 times in her speech accepting the party’s nomination.

In last year’s presidential campaign, Kamala Harris, the vice president and Democratic candidate against Donald J. Trump, boasted of owning a Glock pistol, and left little doubt about her belief in military might as she accepted her party’s nomination in Chicago.

“As commander in chief, I will ensure America always has the strongest, most lethal fighting force in the world,” she said.

But some efforts to escape the Carter legacy only seemed to reinforce it.

Michael S. Dukakis, the former governor of Massachusetts, was ridiculed when he donned a green tank helmet and “military coveralls over his Filene’s suit,” as a New York Times report said at the time, to ride a 63-ton M1 tank around a field at a manufacturing plant in front of a battery of television cameras. “Rat-a-tat,” Mr. Dukakis said.

“Dukakis was trying to demonstrate strength,” Mr. Shrum said. “Instead, he demonstrated weakness. People are always fighting the last campaigns, and they are often wrong.”

In the case of Mr. Kerry, who, like Mr. Kennedy, was a Shrum client, Republicans sought to turn his decorated military record against him by accusing him of fabricating details of his Navy service, in an advertising campaign — later discredited — that was launched by a group calling itself Swift Boat Veterans for Truth. (One producer of those ads was Chris LaCivita, a co-manager of Mr. Trump’s 2024 campaign.)

To be fair, the seeds for this line of attack against Democrats predated Mr. Carter: In 1972, four years before Mr. Carter burst on the national scene, Republicans invoked the “weak on defense” argument against George McGovern, the Democratic senator from South Dakota, when he challenged Richard M. Nixon for the presidency.

“The 1972 presidential campaign and the landslide defeat of McGovern made the weak-on-defense argument a centerpiece for the G.O.P.,” Mr. Zelizer said. “The problems that Carter faced in the final year — Iran and the Soviet invasion of Afghanistan — cemented this political imbalance, placing Democrats in a position to constantly stress that they would be tough on defense.”