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.