The FDNY said that about 20% of members were out sick with symptoms of COVID-19.
"We have thousands of people that are sick. Thousands that are dying," Oren Barzilay, president of FDNY-EMS Local 2507, told ABC News on Tuesday. "It's all over our city. It's not just an isolated case. It's all around us."
Barzilay said that the city had even broken a record for 911 calls Monday -- 7,200 calls -- passing Friday's record of 7,100.
He said that while his workers were "still holding the line" and doing what was necessary to save lives, they were short on personal protective equipment and needed a lot of supplies.
"We want people to be mindful when they call 911. ... We're dealing with severely ill people at the moment that need our attention," he said. "The hospitals are overwhelmed as we are overwhelmed."
ABC News followed EMS at a safe distance in Queens on four calls on Tuesday, including two reports of fever and cough, a COVID-19 patient and a person who had died. As they arrived for each call, EMS workers wore thin, blue gowns, gloves and masks.MORE: Inside the coronavirus 'Ground Zero': Elmhurst Hospital in New York City
During one call that ABC News witnessed, Tracy Sims stood outside as EMS workers entered the home of her aunt who'd been diagnosed with COVID-19 the previous week.
Sims told ABC News that her aunt's doctor had sent her home so she could self-quarantine but that the aunt, who's in her 60s, also had a touch of pneumonia and was feeling winded and short of energy.
"If you're having trouble breathing and, you know, you're an older person, you're by yourself, who's going to go inside to help her?" Sims said to ABC News. "Nobody can go inside to help her."
Barzilay said that Local 2507 had roughly 4,500 EMTs/paramedics with the New York Fire Department, including officers. Of those, he said more than 500 were showing signs and symptoms of COVID-19 and more than 50 members had tested positive for the virus.
The FDNY confirmed to ABC News that more than 20% of the EMS workforce was out sick. The Federal Emergency Management Agency was sending a contingent of paramedics and ambulances to help backfill.
John Rugen, a 16-year veteran with the fire department, described the situation for EMS workers as "madness."
"There's no other way to put it," he said.
Rugen said that when EMS workers arrived at a call, they went in suspecting that everyone in the home or at the scene had COVID-19 in order to protect themselves.
He said that while his station had gloves and N95 masks, it was running short. He told ABC News that he'd even called some stations last week and learned that they didn't have any masks left.
For Rugen, going out every shift puts him at risk. He said he had stage 4 lung cancer from Sept. 11 and that even cigarette smoke could close his lungs.
"This could attack me and kill me because I have shortage [of] lung capacity," he said of COVID-19.
Yet, he said, he worked because he liked taking care of people and had been working with the department since he was 16 years old.
Rugen said he'd even decided to stop seeing his son, who has an underlying medical condition, to prevent him from possibly catching the virus. Rugen said he still Skyped with his young son whom he had not seen for a week.
"It's hard," he said. "Very hard."
Barzilay said that Rugen's decision was a common one among city EMTs. Barzilay said that other members of the service were afraid to go home and chance putting their family members at risk.
"They're sleeping in their cars. We have dozens and dozens and dozens of members who are sleeping in their cars. ... They rather stay here, sleep in the car, wash up and go do it again," he said about working their shifts, which ranged from 16 hours to 20 hours long.
Sims, whose aunt had been diagnosed with COVID-19 and got assistance from EMS Tuesday, told ABC News that she was terrified.
"I'm scared for her. ... I'm scared for me. For everybody. ... It's emotionally taxing," Sims said. "I want this thing to be over."
This report was featured in the Wednesday, April 1, 2020, episode of "Start Here," ABC News' daily news podcast.
"Start Here" offers a straightforward look at the day's top stories in 20 minutes. Listen for free every weekday on Apple Podcasts, Google Podcasts, Spotify, the ABC News app or wherever you get your podcasts.