Puerto Rico has long depended on those ties as people left for the mainland, where, especially in and around New York City, the community has become deeply entrenched and gained political influence over the course of several generations. “The greatest hope for Puerto Rico is its diaspora,” said José Cálderon, the president of the Hispanic Federation, a national advocacy group. “If we’re going to get Congress to do the right thing,” he said, referring to aid, “it is going to be the diaspora that does it.”

Officials and nonprofit groups in Puerto Rico say the immediate need remains for essentials like food and water. But some are already taking stock of the far more enormous investment a full recovery will surely require: rebuilding a health care system and energy grid that had been fraying before the hurricane and are now a shambles, and relief from a debt crisis that had set off its own wave of devastating consequences, including forcing officials to declare a form of bankruptcy this year and spurring an exodus.

As residents of a territory of the United States, Puerto Ricans are American citizens, but they have little clout in Washington: They cannot vote for president in the general election and their delegate in Congress is a nonvoting member. “Is that a disadvantage? Absolutely,” said Edwin Meléndez, the director of the Center for Puerto Rican Studies at Hunter College, who noted that the island could be better served by having its own voting members in Congress. Still, he added, “you have this other network of elected officials that mitigates that lack of representation.”

That network has not always served as a unified force. (Five of the 43 Latino members of Congress are Puerto Rican and all are in the House.) The financial crisis, for instance, was an issue that sowed division. But the storm’s toll has brought many of these politicians together in championing a relief effort. In New York, such efforts have been encouraged by the city’s Puerto Rican community, a significant bloc of support for Puerto Ricans running for elected office.

“It’s not a monolith in terms of thinking,” Mr. Cálderon said. “But the hurricane has taken things to a different plane,” he added. “It’s heartening to see the community functioning and thinking as one and committed to what’s important here, which is to get Puerto Rico back on its feet and running and having a resurgence.”

Some have been more critical than others of the federal response. Jenniffer González-Colón, the territory’s nonvoting congressional delegate, has argued that the federal government had been swift in deploying assistance and that Mr. Trump was “supporting Puerto Rico all the way.”