MISSION, Kan. (AP) — A long line of seniors, some clutching walkers, waited in the cold this week when Kansas' largest county began vaccinating its oldest residents against the coronavirus.

Johnson County, which blamed the long-wait mishap in part on people showing up without appointments, isn't alone in struggling with demand as the state moved beyond vaccinating health care workers and long-term residents. Health officials and hospitals are being deluged with calls, and appointment slots are filling up in minutes.

“We are pleased to see the enthusiasm and the interest in vaccines," County Manager Penny Ferguson said in apologizing for the logistical problems that occurred Tuesday. The situation improved later in the week.

The challenge is that the second phase is massive, including about one-third of the state's 2.9 million residents. It prioritizes those 65 and older, essential workers including teachers and police officers, and those living in communal settings such as prisons and homeless shelters.

Health officials say there isn't enough vaccine to immunize everyone in the second phase quickly. And messaging is tricky because the state is allowing individual counties to decide who goes first within that phase.

As of Friday, just 5.8% of the state’s population, or nearly 168,341 people, had been vaccinated, state health officials said.

“I think one of the things that has happened is it is so confusing to people about where to go to get vaccination because of probably a lack of transparency and good communication," Dr. Steve Stites, the chief medical officer at the University of Kansas Health System, said during a webcast. “People are so frustrated because they want the vaccine right now."

He said his own health system found itself with leftover doses after vaccinating its employees because some of them didn't want to be immunized yet. The health system then provided some of the unused vaccines to nearby health departments but still had 2,000 or 3,000 doses left. It turned to its own patients who were 65 and older and prioritized them based on a random number generator.

“But what that did is it made 2,000 or 3,000 people super happy and like 100,000 people really mad," he said. “And it’s not that it's a bad attempt. The problem isn’t that we don’t want to give it. The problem is we do not have it to give it."

As vaccine supply runs low, the state on Friday reported its smallest increase since Oct. 23, adding 2,168 cases over two days to increase its pandemic total to 274,685. In November, state health officials were routinely reporting about three times that number of cases in a two-day span. The state also reported 61 more COVID-19 deaths since Wednesday, pushing the state’s death toll to 3,779.

In the Lawrence area, health officials sent out text alerts to 1,300 randomly selected people who were 65 and older, inviting them to a drive-thru clinic. Issues surfaced when more than 300 additional people showed up at Lawrence Memorial hospital, many of them spouses and elderly parents of the people who received the invitations.

The hospital, which offered the drive-thru clinic service from Tuesday through Friday this week, worked with the county to obtain more doses so it wouldn’t have to turn away anyone who was qualified.

Hospital spokeswoman Rebecca Smith said the situation illustrates the demand, noting that she receives hundreds of phone calls and emails daily from people inquiring about how they can get vaccinated.

“When you look at the community, there is an incredible and intense desire to be vaccinated as soon as possible, and that is amazing. That is a community that knows and understands the importance of the public health initiative," Smith said. "And our goal is to ensure that as soon as vaccines are available that we can get them into arms as quickly as possible because that's what our patients want. That's what our community wants."

But she added: “It depends entirely on our ability to get vaccine. We can vaccinate 750 people a day or zero. It depends. Do we have vaccines in hand?"