After spending much of the last week out of public view while President Biden was besieged by Democratic doubts, former President Donald J. Trump reveled in Mr. Biden’s struggles and the Democrats’ infighting at a rally on Tuesday evening at his luxury golf resort in Doral, Fla.
“Joe’s own party wants him to throw in the towel and surrender the presidency after a single 90-minute performance,” Mr. Trump said.
Then, he added, in a clearly insincere display of sympathy toward Mr. Biden, “it’s a shame the way they’re treating him. But don’t feel sorry for him. He’s a very bad guy.”
However, in a reflection of the mounting speculation by Democrats and political analysts about whether Mr. Biden will keep his place as his party’s presumptive nominee, Mr. Trump also spent a significant amount of time attacking Vice President Kamala Harris, considered to be Mr. Biden’s likeliest successor should he step aside.
Until recently, Mr. Trump had spoken little about Ms. Harris during rallies and interviews. And even as he repeatedly assailed her, he frequently mispronounced her name, stressing the wrong syllable.
But on Tuesday, he unveiled a new nickname, “Laffin’ Kamala” — which he made sure to detail for the thousands of supporters who waited for hours in Miami heat — and spent several minutes portraying her as ineffective and directly linking her to Biden administration policies he often criticizes.
“She was put in charge of the U.S. border, security at the border,” Mr. Trump said of Ms. Harris. “And she never showed up.”
And in an effort to portray Ms. Harris as unpresidential and unfit to lead, he insisted that Mr. Biden’s selecting Ms. Harris as his vice president was the only thing keeping him in office.
“If Joe had picked someone even halfway competent” as his No. 2, Mr. Trump said, “they would have bounced him from office years ago.”
Mr. Trump has throughout his third presidential campaign depicted Mr. Biden as a corrupt mastermind while also repeatedly questioning whether he was mentally fit enough to serve as president.
On Tuesday, he repeatedly cited Mr. Biden’s halting debate performance as evidence of both of those claims.
Mr. Trump, who was charged in federal court with conspiracy to defraud the United States government over his efforts to overturn the 2020 election, accused Democrats of leading a “sinister plot to defraud the American public” about Mr. Biden’s health. He also repeated his lies that the 2020 election was stolen from him.
He also challenged Mr. Biden to another debate, which he claimed would give Mr. Biden “the chance to redeem himself in front of the entire world.”
And weeks after the two fought over their golf game during the debate, an off-topic digression widely seen as a low point, Mr. Trump tauntingly challenged Mr. Biden to a charity golf game on the course where he was giving his speech.
In a statement, the Biden campaign called Mr. Trump’s rally “deranged” and mocked him for staying out of public view for more than a week.
“Joe Biden doesn’t have time for Donald Trump’s weird antics — he’s busy leading America and defending the free world,” James Singer, a spokesman, said in a statement. “Donald Trump is a liar, a convict and a fraud only out for himself — par for the course.”
As is often the case, Mr. Trump strewed insults throughout his speeches. He said that Democratic candidates were “mentally deficient,” a term he said he was using because a different term was “too tough.”
He mocked Mr. Biden’s physicality and Ms. Harris’s laugh, and he insisted without evidence that those crossing the border were “bloodthirsty terrorists, savage gang members and child predators” or escapees from mental institutions whom he compared to the fictional serial killer Hannibal Lecter.
And Mr. Trump once again suggested he might prosecute his political enemies if elected in November. After he baselessly accused Mr. Biden of orchestrating the four criminal cases brought against him, Mr. Trump said that Mr. Biden “has unleashed a horrible thing, because that can happen the other way around too.”
Mr. Trump, who vaulted to national prominence because of a reality show in which he pitted competitors against one another for his approval, also exhibited his competitive side as he alluded to picking a running mate.
The deadline for Mr. Trump to select his partner on the ticket is fast approaching: His running mate will be formally nominated during the Republican National Convention, which starts on Monday in Milwaukee. Advisers have said Mr. Trump will most likely make his selection known before the convention begins.
Ahead of Tuesday’s rally, the Trump campaign teased a possible running-mate announcement in fund-raising emails. And speculation deepened because of the attendance of Senator Marco Rubio of Florida, one of Mr. Trump’s top contenders.
Mr. Trump appeared to enjoy dangling the possibility of his selecting Mr. Rubio, whom he viciously competed against during the 2016 primary, as his running mate.
After talking about his proposal to remove taxes on tips for hospitality workers, he urged Mr. Rubio to vote for it. Then, he added cheekily, “well, you may or may not be there to vote for it.”
And at another point, after commenting on the crowd of reporters in the press pen, he looked to Mr. Rubio, saying, “I think they probably think that I will be announcing that Marco is vice president.” Then he immediately returned to his usual spiel about the economy, as if the moment hadn’t happened.
Mr. Rubio had so far this year appeared infrequently on the campaign trail with Mr. Trump. In his remarks, delivered hours before Mr. Trump took the stage, he did not acknowledge the possibility of his being the former president’s running mate.
Instead, Mr. Rubio used his time to echo Mr. Trump’s mocking of Mr. Biden’s debate performance and his frequent attacks that Mr. Biden was not mentally fit to lead the country.
Like Mr. Trump, he also directly attacked Vice President Kamala Harris, mocking her laugh and calling her “a real life, verified left-winger.” Being able to hold one’s own against the vice president in a potential debate is seen by his camp as a prerequisite for Mr. Trump’s partner on the ticket.
And Mr. Rubio also made a point to address the crowd in Doral, which included many Hispanic Americans, briefly in Spanish, perhaps highlighting how he might help Mr. Trump make inroads with Latino voters.
Several in attendance at the rally said that they did not care much who Mr. Trump picked, saying they trusted his judgment to add the right person to the ticket.
”He’s practical,” David Kim, 45, said.
Richard Siu, 57, said he liked the idea of Mr. Rubio as Mr. Trump’s running mate. But he downplayed the importance of the pick, saying he’d back anyone Mr. Trump chose.
“It’s good for President Trump, OK, then it’s good for me,” said Mr. Siu, who lives in Miami.
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