The governor's emergency trip comes as hundreds of thousands of people remain without power and water. Many are staying in shelters, because they're fearful to return home.
"They are dealing with anxieties that almost every hour they feel tremors, every morning. Even though they have sound structures of households, they're sleeping outside," said Bronx Borough President Ruben Diaz Jr., who has family on the island.
CBS2's Tony Aiello is in San Juan, Puerto Rico, where he met one family getting ready to leave, 20 members forced from their homes and heading to Springfield, Mass.
Damage tops $100 million and is focused along the island's south coast. Workers from New York are expected to help get the Costa Sur power plant operating again since it was knocked offline when the earthquakes began.
The government knows quickly restoring power is a key task which it failed to do two years ago after Hurricane Maria.
Cuomo said 115 National Guard members will survey the damage and distribute supplies, including hundreds of blankets, pillows and emergency preparedness kits.
"This is our family, and our family is in trouble. What do we do when a family member's in trouble? We come together, we pull together and we work to help one another," he said before his flight. "We'll make sure that Puerto Rico is not left on its own."
While millions wait to see whether President Donald Trump will sign a major disaster declaration to authorize much-needed aid to the island, FEMA's top official in Puerto Rico told CBS News, "We're not waiting."
"We've got our teams out in the field," said Alex Amparo. "A tremendous amount of mutual aid that's happening from the island."
Meanwhile, local churches, non-profits and businesses, like one South Bronx gym, are collecting supplies for those in need.
"We make sure that it gets to the right people in Puerto Rico," an organizer said Monday.
The governor left from John F. Kennedy International Airport Tuesday morning and will return Wednesday.
While in Puerto Rico, Cuomo toured quake damage by air and on the ground.
"You know, you see thousands of people who have left their homes, either because of damage to their homes or fear that they don't want to stay in their homes because they don't know if there's another earthquake, they don't know if there's damage to the home or if the home could survive another tremor," said Cuomo.
Meanwhile, New York City Mayor Bill de Blasio is also sending city resources, including building inspectors, engineers and emergency managers, to provide support.
Much-needed supplies arrived Tuesday evening at Ponce High School, which is now sheltering hundreds of earthquake refugees.
Adrian Medina was on the ninth floor of a condo when Saturday's big one hit Ponce.
"People were screaming, running all over the place," he said.
Nearby Guánica was devastated. Many homes and vehicles were damaged or destroyed when the earth shook.
Hector Torres suffered a terrible loss. A wing of his home collapsed, the ceiling falling down towards the floor.
"I don't think it can be repaired. Everything is cracked," he said.
After the one-two punch of Hurricane Maria and now earthquakes, residents are under stress.
Back at the shelter, former Bronx priest Roberto Gonzalez Nieves offered words of comfort. He's now Archbishop of San Juan.
"It's quite moving to witness the resilience of people, their deep faith, the way people come together to help one another," he said.
Every night, people at the shelter sing and pray. Times are tough, but they are staying together.
The mayor of San German, Puerto Rico, tells CBS News psychologists and other mental health providers are needed for survivors. He said that's the only thing he's asking for.
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