The lines are endless and hospital telephones are ringing off the hook since coronavirus vaccines became available this week for the elderly in retiree-rich Florida.

The state government gave the green light Monday for inoculating those aged 65 and above -- a group that makes up nearly 20 percent of the Sunshine State's population, the largest such proportion in America.

So ever since, it has been mayhem, as tens of thousands try to get a shot they hope will protect them against the potentially deadly Covid-19.

Governor Ron DeSantis has asked for patience, admitting that at least for now, there are not enough doses for every elderly Floridian.

"The Covid vaccine supply is limited," he told a press conference on Wednesday in a retirement community in Palm Beach.

"We don't have enough vaccine on hand for all four million-plus senior citizens. We will get there."

The Jackson Health System said that this week, it hopes to vaccinate 10,000 of its 65-plus patients and individuals at high risk due to pre-existing conditions. Next week, it will help patients outside its system.

It kicked off its campaign with a few local celebrities getting the jab -- musician Emilio Estefan (husband of Gloria), 67, and former Miami Dolphins player Nat Moore, who is 69.

Estefan defended the need for people to get inoculated, amid ongoing speculation about how effective it is.

"I think there's a lot of misinformation out there," Estefan told reporters at the headquarters of the Jackson Health System, the largest hospital network in Miami.

North of Miami, in Fort Lauderdale, Broward Health got such a flood of calls that it said its appointments for vaccinations are now filled up until February.

The Broward County webpage for making a vaccination appointment has been down since Wednesday.

Things are just as frantic in central Florida: in Orange County, which includes Orlando, home to Disney World, officials said they have scheduled 30,000 vaccinations and can make no more appointments for now.

'I can't wait'

So far, more than 175,000 people have received their shots, according to the state health department.

But for some, after nearly a year of various lockdown restrictions, the wait feels unbearably long.

"I can't wait to see my grandkids. I can't wait to hug those little guys. It's just been so long," Candice Seltzer, a retiree who has been vaccinated, told CNN.

Since vaccines were first distributed in mid-December, from Pfizer-BioNTech and then from Moderna, the majority of doses went to health care workers, and nursing home residents and staff.

Last week, DeSantis extended the campaign to include everyone aged 65 and above, and patients with serious health complications.

So far, Florida has recorded more than 1.3 million coronavirus cases and more than 21,500 deaths. It has recently been notching up as many cases each day as it did at its previous worst moment of the pandemic, in July.