MIAMI — For 60 years, the lifeblood of Miami’s idiosyncratic politics has been Cuba, the communist government’s countless sins denounced in street protests, dissected on the spirited Spanish-language airwaves and condemned at campaign rallies under the unifying cry of “Viva Cuba Libre!”

But the focus of this city’s freedom-loving fervor has recently moved further south.

Venezuela, not Cuba, now dominates Miami’s political conversation. A television anchor not long ago ended a somber segment with a promise to keep praying for the troubled South American country. Venezuelans in the city have gathered for demonstrations to coincide with protests back home. Even the Miami-Dade County Commission, a local body with no control over foreign policy, voted unanimously to recognize the opposition leader Juan Guaidó as Venezuela’s interim president.

The shift has been coming on gradually for years, but it has accelerated in recent weeks as Venezuela has sunk further into crisis and its leftist president, Nicolás Maduro, has clung defiantly to power. The showdown in Caracas is reshaping Latino politics in South Florida, home to the highest concentration of Venezuelans in the United States.

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.