ORLANDO, Fla. — When health officials suggest they’ve got a long way to go in vaccinating all Floridians against COVID-19, they mean it: The number of people vaccinated so far in Greater Orlando wouldn’t fill Camping World Stadium.

Some 36,151 people in Orange, Seminole, Osceola, and Lake counties received vaccinations through Sunday, according to an online vaccine summary from the Florida Department of Health. That represents 1.4% of a population of about 2.5 million.

Statewide, 260,655 people — 1.2% of an estimated 21.9 million — had been vaccinated through Sunday.

Those numbers preceded a visit to Central Florida on Monday from Gov. Ron DeSantis, who sought to assure residents that his office was mobilizing efforts to administer vaccines as quickly as possible. DeSantis also emphasized that he would prioritize seniors during this second phase of vaccine distributions.

His visit came as COVID-19 cases in Florida approached 1.4 million, residents reported crashes of vaccination registration sites, and supply of vaccines from Pfizer and Moderna hadn’t met demand across the state.

The frustration and angst for residents continued Tuesday as the Florida Department of Health in Polk County declared its vaccination appointments booked and its phone system overwhelmed. In Volusia County, a vaccine site cut off its line for a second straight day, delaying shots for senior residents who said they had spent the night in their cars.

Officials at Orlando Health said at the DeSantis news conference that they expected this week to administer 20,000 vaccines to a range of people. Those included health care professionals employed outside of Orlando Health, plus residents at nursing homes, long-term-care, and assisting-living facilities.

Hours later, Orlando Health announced that it had reached its appointments limit for vaccines and that it would reopen registrations when it received additional doses.

“We are planning to further expand the program in the coming weeks as more vaccines become available, to reach more individuals 65 years of age or older, as well as those at increased risk of contracting the virus due to chronic medical conditions,” Orlando Health spokeswoman Kena Lewis wrote Tuesday in an email reply to questions from Spectrum News 13.

Lewis said Orlando Health also seeks ways to transition its vaccination program to settings such as clinics, which she called “more accessible to the public than the hospital environment.”

During his visit, DeSantis urged hospitals to expand vaccination services to seven days a week and said the state had distributed the vaccine to all county health departments, in addition to hospitals.

On Tuesday, Seminole County said it had received a shipment of 12,675 Pfizer vaccines and declared itself among 11 Florida counties to receive a second vaccine shipment.

Also Tuesday, Orange County said it received 19,500 doses of the Pfizer vaccine. Kent Donahue, spokesman for the Florida Department of Health in Orange County, told Spectrum News 13 in an email that county health workers since December 26 had provided more than 6,900 vaccinations to EMTs, paramedics, and people age 65 and older who made an appointment.

DeSantis said Monday that health officials in Palm Beach County in recent days administered hundreds of vaccines to seniors.

“This is the type of thing that we’re going to replicate at other senior living communities across the state,” he said.

DeSantis also announced four initiatives to speed up the distribution process. On Tuesday, he announced that Publix would administer vaccinations in Marion, Citrus, and Hernando counties.

Asked what measures AdventHealth — last month among the state’s first hospitals to receive the Pfizer vaccine — was taking, spokesman Jeff Grainger told Spectrum News 13 that the hospital chain planned an announcement later this week.