Meanwhile, the elderly and front line workers have to scavenge to find a dose.
At Brookdale Hospital, everyone in line by 2:30 p.m. Friday was told they made the cut.
"I'm so happy to here. I'm so happy. I'm ill anyway, so I just really need the vaccine," Gail Finley, of Sheepshead Bay, said.
Since Tuesday, the hospital has provided COVID vaccines to anyone who can prove their eligibility, no matter where they live, no appointments needed.
"My sister found out from a neighbor," New Jersey resident Dale Muken said.
Thursday and Friday alone, the hospital administered 1,200 doses, but it's unclear how long that can last.
- New York State book online here or call 1-833-NYS-4-VAX
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- New Jersey book online here
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De Blasio warns the supply at city-managed sites is set to run out.
"We will run out next week. I'm telling you, at this rate, there will not be any doses left in the city of New York at the end of next week if we don't get a major re-supply," he said.
That supply comes from the federal government, which expanded eligibility without providing more vaccines.
"What you can't get past mathematically is 7 million people chasing 250,000 doses. That is the mathematical problem that you can't solve," Gov. Andrew Cuomo said.
And what's left is going fast.
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At George Wingate High School in Brooklyn, a new vaccination site has opened for city employees.
"We're arguing, advocating for doses everyday. We're in constant contact not only with the city, with the state and now with the new federal administration," said Henry Munoz, with SOMOS Community Care.
The fear is more sites will be forced to temporarily close, like the one at Brooklyn Army Terminal.
"We're calling by phone two, three times a day. Each call takes an hour, an hour and a half. And they say sorry, we don't have vaccines," Brooklyn resident Juan Suarez said.
Watch Aundrea Cline-Thomas' report --
The mayor says if you already have your first dose, you should be able to get your second dose at the same location.
The potential shortage is for first doses only.
Brookdale Hospital will resume providing vaccines next Wednesday.
Meanwhile, New York City isn't alone in its shortage. Other counties are also struggling.
Living alone in Nyack and still cooking her own meals, 95-year-old Jean Kelly does her best to lead a healthy lifestyle.
"I think I have a good diet. I drink two glasses of wine every night, which helps," Kelly said, laughing.
The family of this witty great-grandmother wants to make sure she stays well by getting the COVID vaccine, but trying to book her an appointment has become a second fulltime job for son Chris Kelly.
"I'm on that site all day long," he said.
From the state website crashing constantly and calls to the vaccine hotline going unanswered, it's one discouraging dead end after another.
Finally, they secured an appointment, but it's in another county, two and a half months from now.
"To get people vaccinated, where and when and this rollout... I think it's been, it's a huge failure," Chris Kelly said.
"What are people supposed to do? Where are people supposed to go?" CBS2's Jessica Layton asked Rockland County Executive Ed Day.
"The problem is there are no options here," Day said. "We've been advising them, if you see a location in the city, go."
Day is fed up. He says this week, the state only sent 10% of the doses they asked for. They've run out of the vaccine altogether.
"We need this vaccine. People are going to die unnecessarily," he said.
CORONAVIRUS: NY Health Dept. | NY Call 1-(888)-364-3065 | NYC Health Dept. | NYC Call 311, Text COVID to 692692 | NJ COVID-19 Info Hub | NJ Call 1-(800)-222-1222 or 211, Text NJCOVID to 898211 | CT Health Dept. | CT Call 211 | Centers for Disease Control and Prevention
He wants to know why the state is opening up sites like the Javits Center if it can't supply to the counties.
"My mother's not the only 95-year-old person who is waiting," Chris Kelly said.
"It worries everybody. I think it's in everybody's mind," Jean Kelly said.
Until manufacturers pump out more vaccine and poor planning improves, the vulnerable, like Jean Kelly, remain caught in the middle of the supply struggle.
CBS2's Aundrea Cline-Thomas and Jessica Layton contributed to this report.
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