In many ways, with Mr. Atwater as its dark prince of strategy, the Bush campaign of 1988 marked the birth of the modern-day negative campaign. Most memorably, Republicans plastered Mr. Dukakis, then the governor of Massachusetts, with the case of Willie Horton, an African-American man who raped a white Maryland woman and stabbed her boyfriend while on a Massachusetts prison furlough program.

As President Trump faces similarly daunting poll deficits in his contest with Joseph R. Biden Jr., he is running one of the harshest campaigns since Mr. Bush defeated Mr. Dukakis, and Republicans are looking back at the 1988 race as a beacon of hope in a bleak political landscape. For all the differences between the Democratic nominees in 1988 and today, Mr. Dukakis’s collapse in the face of an onslaught by Mr. Bush has long stood as a lesson in how quickly public opinion can change, how summer polls can prove ephemeral, and how an artfully executed party convention can help turn around a struggling campaign.

As Republicans gather in the coming week to nominate Mr. Trump for a second term, the president and his political and media allies have torn into Mr. Biden and particularly his running mate, Senator Kamala Harris, including making racist and sexist attacks. There is a direct line between the hard-edge campaign Mr. Bush ran portraying Mr. Dukakis as a far-left liberal — and the racial undertones personified by seizing on Mr. Horton — and the Trump campaign that is emerging today.

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But if the 1988 race offers a cautionary tale for Mr. Biden, there are some critical differences between that race and the current campaign that is now moving into high gear as Democrats finished their convention last week and Republicans step on to the mostly virtual stage.

Mr. Biden is far better known than Mr. Dukakis was and he has shown a resilience to caricature that Mr. Dukakis did not have. Mr. Trump is viewed unfavorably by a big swath of voters, in no small part because of the coronavirus pandemic that has killed more than 175,000 people in the United States and devastated the economy on his watch. His lack of credibility with many Americans has undercut his ability to deliver an attack.

The nation is more pessimistic than it was when Mr. Dukakis faced Mr. Bush, who as Ronald Reagan’s vice president was effectively running as an incumbent. A New York Times/Siena College poll in June found 58 percent of respondents said the nation was headed on the wrong track. In the fall of 1988, a significantly lower 46 percent of registered voters said the nation was going in the wrong direction, according to a Washington Post/ABC News Poll.

“This is going to be tricky for them: Biden is a pretty well-known quantity,” said Susan Estrich, who was Mr. Dukakis’s campaign manager. “The way you usually burst balloons is paint the other guy as a risk.”