Barbara Shlevin has kept a running tally of calls she made in search of the coronavirus vaccine. By Wednesday, she had tried the health department and a hospital system in Broward County, Fla., 184 times.

Only once did the 71-year-old retired librarian get through. She said she waited more than 10 minutes, and finally heard a voice on the other end of the line. Then, the call cut off. So, she started trying online.

For days after Florida Gov. Ron DeSantis (R) announced that the potentially lifesaving vaccine would be available to seniors, Shlevin had no idea when she and her husband would have a chance at it.

“You had at least six months to get ready. You could have figured out a better way to do this,” said Shlevin, of Pompano Beach, Fla. “It shouldn’t be this hard.”

After months of anticipation, millions of doses of the two authorized coronavirus vaccines — made by Pfizer-BioNTech and Moderna — are flowing into hospitals and health departments across the nation, putting the end of the pandemic in sight. But Americans trying to access shots are encountering systems that vary widely county to county and that, in many places, are overwhelmed.