Florida would seem to be fertile territory for Mr. Biden, given that the Inflation Reduction Act, which he signed into law after it passed on party-line votes this summer, caps out-of-pocket prescription drug expenses for Medicare recipients, limits the cost of insulin and empowers the government to negotiate lower prices with pharmaceutical companies, longtime goals of many older Americans. “We beat Big Pharma,” Mr. Biden said on Tuesday.

But when national Democrats talk about states where they believe they have good prospects next week, Florida does not make the list. Even though statewide races have been close in recent cycles, Democrats have felt burned by narrow losses and have been reluctant to invest the sizable amounts of money required in a state with so many media markets only to be disappointed again.

In addition to Mr. Crist, who is seeking to oust the incumbent Republican governor, Ron DeSantis, Mr. Biden appeared with Representative Val B. Demings, the Democratic challenger to Senator Marco Rubio. Mr. DeSantis leads by roughly nine percentage points and Mr. Rubio by about seven percentage points, according to an aggregation of polls by the political data website FiveThirtyEight.

Democrats chose a modest arena at Florida Memorial University, a historically Black college, for the rally, assembling a far smaller crowd than typically mustered by former President Donald J. Trump, a Florida resident.

Addressing a largely Black audience, Mr. Biden boasted of his nomination of Justice Ketanji Brown Jackson and other diverse appointees. “Guess what? I promised you I would have a Black woman on the Supreme Court,” he said. “She’s on the Supreme Court. And she’s smarter than the rest of them.”

He went after some Republicans by name. He called Mr. DeSantis “Donald Trump incarnate.” He accused Representative Kevin McCarthy of California, the would-be new speaker, of being “reckless and irresponsible.” And he assailed Republicans like Representative Marjorie Taylor Greene of Georgia, the onetime QAnon follower who has worked to push the party to the right, for criticizing his effort to forgive some student loan debt while having their own Covid-19 loan debt forgiven.

The president appeared most irritated by attacks on him over inflation. In Hallandale Beach, he pointed to his efforts to limit health care costs for seniors. “They talk about inflation all the time,” he said. “What in God’s name?” He added: “If you have to take a prescription and it cost you an arm and a leg and I reduce that, you don’t have to pay as much. That reduces your cost of living. It reduces inflation.”

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