NEW YORK (CBSNewYork) — New York State entered the next phase of coronavirus vaccine distribution Monday, with millions more residents now eligible for their shots

This comes as the state expands the number of sites where people can roll up their sleeves.  But from computer glitches to not being able to get anyone on the phone, it’s not running as smoothly as many had hoped, CBS2’s Jenna DeAngelis reported.

The state entered Phase 1B Monday, meaning the largest group — 3.2 million people — are eligible for the vaccine. The group includes people 75 and older, first responders, public safety workers, public transit workers and education workers.

In addition to being eligible for the vaccine, you must make an appointment to get into any of the city’s 160 vaccination sites.

Hillcrest High School in Flushing, Queens is one of them. DeAngelis reported seeing people without appointments getting turned away, but also said the line was steady all day.

“It is worth the wait,” said medical worker Mary Joy De Leon, a Battery Park City resident.

De Leon waited in line for an hour for her vaccine appointment, which she made online.

“It’s very straightforward, with an appointment ID number,” she told DeAngelis.

She felt, “relieved” when she finally got into the chair to get her first dose of the vaccine.

“I’m more confident now going to work on a day-to-day basis, exposing myself to other people,” De Leon said.

While some found the process of booking an appointment and getting the shot easy, others did not.

Harris Ton, whose mother is a lung cancer patient, eagerly waited for the moment his mother was allowed to get her first dose of the COVID vaccine.

“I’m feeling great. I’m very excited,” he told CBS2’s John Dias at the new mass vaccination center in Sunset Park, Brooklyn.

Watch John Dias’ Report:

But hope was met with frustration and long lines at the Brooklyn Army Terminal, one of the city’s first 24/7 vaccine hubs.

“I don’t know what we are supposed to be doing,” one person said.

Many who registered online were trying to make their appointment in-person since they had trouble on the city’s website.

They were turned away and told the hubs don’t take walk-ins.

“This website, it just keeps loading, keeps loading, when you try to secure an appointment. It doesn’t go anywhere,” one person said.

“I got to take my granddaughter or my daughter to make an appointment,” said Walter Costas, who doesn’t have a computer and needs an appointment for himself and his wife.

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Annette Fisher, a senior advocate, said it was confusing even after she was finally able to register three of her clients on the website. Fisher said they had no chance of getting vaccinated when they arrived.

“It gave all three receipts. So I said, ‘OK, I guess we come here and we just wait on the line. Maybe that’s their idea of making a scheduled appointment.’ It didn’t say, now go make another thing to get a date,” Fisher said.

Other sites across the city had similar problems Monday, but Mayor Bill de Blasio defended the rollout.

“We want to do our best to manage that,” de Blasio said.

The mayor has vowed to set up 250 city-run vaccination sites by the end of January.

“We have navigators that are going to go out there, going to talk you through whether you need an appointment or whether you have one, and they’re going to help you to figure it out,” said Dr. Ted Long of NYC Health + Hospitals. “That’s one of the things we learned from testing.”

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

On Monday, the city announced a phone number where people can make an appointment by calling 877-VAX- 4NYC.

“We want to absolutely embrace seniors or anyone who’s not comfortable online and prefers to make their reservation by phone,” said de Blasio.

“There is also a phone number to use. You can’t get through,” one person told Dias.

More 24/7 mega vaccination sites in Lower Manhattan, Staten Island and Queens are also being planned.

The city is aiming to vaccinate 175,000 people this week, surpassing last week’s 101,000 doses.

“How many people does the city actually have vaccines for and when do you expect the next shipment to come?” DeAngelis asked city officials.

MORE: Mass COVID-19 Vaccination Sites Open In Parts Of New York City Will Operate 24/7 Starting Monday

“We have approximately 230,000 doses on hand today in New York City. We expect to get an additional about 100,000 doses delivered this week,” said NYC Health Commissioner Dr. Dave Chokshi.

“We’re accelerating. We’re going to run out of doses in the next few weeks if we don’t get more of a supply coming in,” said de Blasio.

De Blasio said the city has enough doses to get through this week and into next week, but it could run out unless the federal government steps up.

According to the COVID-19 vaccine tracker, more than 200,000 doses had been administered before Monday.

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CBS2’s John Dias contributed to this report.

Jenna DeAngelis