The battle for Republican presidential delegates jumps Sunday to Puerto Rico, a highly unpredictable contest on an island racked by a deepening debt crisis that could have ripples in the general election.

There are no public polls of voter preferences in the territory, and the remaining Republicans in the race haven’t competed hard for its 23 convention delegates. But political analysts say how the candidates address the crisis could help determine the vote in the battleground state of Florida, home to nearly a million Puerto...