The change is not a mere demographic curiosity. In Florida, where major elections have repeatedly been decided by tiny margins, an inflection point around Venezuela’s leadership could help define a generation of Venezuelan-American voters, who number in the tens of thousands in this state. President Trump is pushing Mr. Maduro to step aside, and if he succeeds, Democrats fear it could transform Venezuelan-Americans into loyal Republicans, much like Cuban-Americans.

“This could be Bay of Pigs 2.0,” said Liz Alarcón, a Venezuelan-American Democrat, referring to the C.I.A.-backed invasion of Cuba in 1961 that failed to overthrow Fidel Castro. The raid turned into a disaster, in part because President John F. Kennedy’s government did not provide sufficient air support to the Cuban exiles who made up the bulk of the invading force — and Florida’s Cuban community turned against both Mr. Kennedy and the Democratic Party.

“It is very dangerous territory for Democrats,” State Senator Annette Taddeo of Miami, a Colombian-American and a Democrat, said of her party’s handling of the Venezuela issue.