The effort that Mr. Scott and Republican allies are waging today is strikingly similar to that multifront war in 2000 led by the George W. Bush campaign and an army of party consultants. Lawyers are filing complaints in Tallahassee; surrogates for the Republican candidate are holding news conference calls with journalists and sitting for interviews on cable, blaming the Democrats for tarnishing the integrity of the electoral process; and party officials are encouraging demonstrators to gather at sites where the recounts are taking place.

“The tactics are the same, the issues are the same, the problems are the same,” said Brad Blakeman, a Republican consultant who worked on the party’s messaging in 2000. “And quite frankly,” he added, “the solutions are going to be the same if no one concedes, because again you’re going to have a court determining the outcome.”

There is one new variable, however: Mr. Trump.

The president, who has long fanned unfounded claims of voter fraud, is especially concerned with the Florida outcome, according to people in touch with him about the recount. And he equates his political success with that of Ron DeSantis, the Republican nominee for governor whose campaign was taken over by Trump aides, as well as with that of Mr. Scott, whose victory he believes he ensured by campaigning across the state and pulling him over the finish line. Mr. Trump sees the recounts, one person close to him said, as akin to a personal attack.

Mr. Trump has been more combative and unrestrained in slinging claims of fraud and unfairness than Mr. Scott or Mr. DeSantis. The recount story hits many of the president’s sore spots, including his frequent insistence that his political opponents cheat against him and his unproved belief that American elections are tainted with illegal voting, especially by undocumented immigrants.

But with such aggressive, unyielding attacks on Democrats, Mr. Trump and his Republicans risk treading into territory that is a minefield of tension over race. Their repeated allegations of subterfuge and fraudulent ballots are a blunt appeal to a political base motivated by the notion that elections are often stolen by Democrats. And in this case, some of the central players are African-Americans, including Mr. Gillum and the Broward County supervisor of elections, Brenda C. Snipes, whom Republicans like Mr. Scott have called out by name for enabling “rampant fraud,” as the governor put it last week.

In the face of the Republican cries of ballot fraud and political mischief, Judge Tuter in Broward County refused a request by Mr. Scott to order the county police to impound voting machines and ballots when they are not in use. The judge was also critical of comments made by Mr. Scott’s lawyers on television and social media perpetuating the unsubstantiated rumors of fraud.