Holding political office in Florida increasingly requires trekking to Puerto Rico, the former home of a growing number of Florida residents. More than a million Puerto Ricans already lived in the state before the hurricane, and another 56,000 joined them in the first six months after Maria, according to an estimate by the Center for Puerto Rican Studies at Hunter College in New York.

Perhaps not all of them will stay, much less vote: Puerto Ricans have tended to cast ballots less reliably than other Florida Hispanics. But if they do — perhaps driven by the slow response to Hurricane Maria — they could emerge as a significant political force, and not just for Democrats. Though Puerto Ricans tend to lean left, many have also registered as Florida voters without party affiliation, giving Republicans an opening to make a play for their support. If Republicans are successful, they could grow their Hispanic conservative base beyond Cuban Americans.

In any case, the arrival of Puerto Ricans has not gone unnoticed in a state where premier election contests have routinely been decided by a single percentage point. The island’s recovery from Hurricane Maria has become an issue of critical concern in Florida, with candidates jostling to appear in touch with the state’s Puerto Rican diaspora.

This election season, it’s not just Mr. Nelson, who is facing a daunting Republican challenge from Gov. Rick Scott, vying for the Puerto Rican vote. Candidates down the ticket are also adopting the island’s cause.

State Representative David Richardson of Miami Beach, a Democratic candidate for Congress, this month spent 48 hours on what he called a “listening tour” of the island. He is running in Florida’s 27th Congressional District, which is nearly 72 percent Hispanic and largely Cuban-American. His campaign research, however, revealed that about 25,000 Puerto Ricans live in the district, he said, so Mr. Richardson felt a trip to the island was in order.