Should Mr. Trump get trounced in South Florida, he might be hard-pressed to make up the difference elsewhere.

Trump supporters believe he can improve upon Mitt Romney’s performance in North Florida, in the conservative panhandle region and in the Jacksonville area. But Mr. Romney found it difficult in 2012 to overcome a catastrophic defeat in Miami. He cut into President Obama’s support across most of Florida, but the president held steady in Tampa and Orlando, two other diverse cities, and expanded his margin of victory in Miami-Dade by about 69,000 votes over his 2008 lead.

Mr. Obama ultimately captured Florida by about 74,000 votes.

Mr. Trump has his supporters here. Norma Samour, the owner of a shopping center, said she was a habitual Republican voter and would likely back Mr. Trump despite some mixed feelings. “He will make the United States more like it was 15 years ago,” said Ms. Samour, 56, who was raised in El Salvador and is of Palestinian descent. “People all over the world used to respect the United States.”

Yet the falloff Mr. Trump faces has, at a minimum, severely hindered Republican efforts to win statewide. Mr. Gimenez, the Miami-Dade mayor, said nominating Mr. Bush or Mr. Rubio would have allowed Republicans to challenge the Democrats’ dominance in South Florida.