FORT LAUDERDALE (CBSMiami) – A third state Department of Health drive-thru COVID-19 vaccination site opened Tuesday for people 65 and over who had made appointments.

People lined up early for their vaccinations at Markham Park in Sunrise. Vaccinations at this location will be given Tuesday through Saturday, from 8 a.m. to 4 p.m.

Two other sites opened last Sunday, Vista View Park in Davie and Tradewinds Park in Coconut Creek will administer vaccinations Sunday through Thursday, from 8 a.m. to 4 p.m.

Barry and Judy Wagner zipped through the Tradewinds Park line, but it took 20 tries to get registered.

“It reminded me of concert tickets, you have to be persistent.”

The first day of vaccinations did not go smoothly at Vista View, people waited for hours and when the site closed early, hundreds were turned away.

The state health department said they would be rescheduled.

Carol Orloff got vaccinated but not her husband. I signed up, but when I tried to sign him up, I got knocked off.

Sandy Orloff is a retired pharmacist who would like to volunteer, but so far no takers.

“I’ve made dozens of calls, nobody gets back to me.”

On Monday, the state’s health department announced on their website, BrowardCovidVaccine.com, that all of their available vaccination appointments had been filled.

“The Florida Department of Health in Broward County has provided 26,465 COVID-19 vaccination appointments to individuals ages 65 and over. All appointments have been filled at this time. Please check back to this website often as more sites and appointments will be added over the coming days and weeks. Thank you.”

The free vaccinations are given by appointment only, no walk-ups allowed. The department said appointments cannot be made by telephone.

Everyone who is vaccinated receives a card with their return appointment for the second and final shot in three weeks. They’re also be monitored briefly to see if there were any bad reactions.

Related: What You Need To Know About Getting The COVID-19 Vaccine In South Florida

On Tuesday, Broward Mayor Steve Geller gave a blunt assessment of the COVID-19 and vaccine situation in the county. He said the bottom line is that seniors will have to be patient.

Geller said there has been a failure by the government in terms of supply and distribution of the vaccine.

The mayor went on to say while Gov. Ron DeSantis had promised seniors they will be getting the vaccine first, the reality is they may not get it until the end of March.

“Every senior that wants a vaccination should be able to get one in the next two to three months – but not tomorrow. It’s important to understand that not everyone will be vaccinated tomorrow, or this week, or this month. And by the way, that two to three-month period assumes that the supply of vaccine holds out, which at this point in time is an unknown quantity,” said Geller.

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A fourth vaccination site at Holiday Park in Fort Lauderdale is expected to open Thursday. No hours of operation have been announced.

A fifth vaccination site will open Friday at Central Broward Park & Broward County Stadium, at 3700 NW 11th Place in Lauderhill. Vaccinations will be given Monday through Friday from 8 a.m. to 4 p.m.

The state’s health department plans to open more sites in the coming weeks.