Puerto Rican airports have become scenes of tearful goodbyes as families send their children, spouses and parents to live with relatives in Orlando, New York, Washington — wherever.

On the mainland, cities and states with large Puerto Rican populations are preparing for the influx by trying to help people find housing, work and schools. Florida alone — already home to 1 million Puerto Ricans — anticipates as many as 100,000 arrivals to the Orlando and the -Tampa Bay area.

In the two weeks since the storm gutted Ms. Gomez’s home on the eastern coast of Puerto Rico and ruined her dreams of renting rooms to tourists, Ms. Gomez said, her family has been surviving on canned food and boxed milk, paid for with the only cash they had on hand — her three children’s private-school fees. Her husband has been waiting in line for hours to buy fuel for their generator. She has been making two-hour trips to buy groceries from a swampy supermarket. Finally, she decided: Enough.

Relatives in Miami offered to buy plane tickets for her and the children, and Ms. Gomez made plans to use the last few gallons of gasoline in her car — it was just enough for the drive to the San Juan International Airport.

Puerto Ricans have streamed off the island for so many decades and in such numbers that migration is woven into Puerto Rico’s identity and culture. One aching anthem pines that “I’m leaving, but one day I’ll return to find my love, to dream again, in my Old San Juan.”