SALT LAKE CITY — Just 12% of Utahns insist they’re never getting vaccinated against COVID-19 but an overwhelming majority believe the state’s vaccine distribution system is fair, according to results released Sunday from a new Deseret News/Hinckley Institute of Politics poll.

More than a third of Utahns say they want to get vaccinated as soon as possible, while another 25% say they’ve already gotten their shots, a number slightly higher than the Utah Department of Health’s dosage count.

Less than 40% of Utahns are either waiting, in no rush, or rejecting the vaccine. Just 3% aren’t sure how they feel.

When it comes to the state’s eligibility list for the vaccine, though, 80% of Utahns agree it’s fair.

The poll was conducted by independent pollster Scott Rasmussen Feb. 10-16 for the Deseret News and the University of Utah’s Hinckley Institute of Politics of 1,000 registered Utah voters and has a margin of error of plus or minus 3.1 percentage points.

Rasmussen said his national polling has shown the majority of Americans who haven’t been vaccinated know someone who has gotten the shots that became available in mid-December after the unprecedented effort that made doses available within months rather than years.

“So this is something that’s now very real. It’s no longer a political theory. It’s no longer a political football,” the pollster said, describing the response to the deadly virus as largely partisan until President Joe Biden took office, despite former President Donald Trump’s false claims that he won the election.

Now, Rasmussen said, people are focusing on what the virus may mean for them. He said his national polling has found many are growing increasingly confident that if they are diagnosed with the coronavirus, they can recover quickly.

‘‘What a lot of people are saying is, ‘There are trade-offs. Yes, it would be good if we reached a point where this pandemic was over. Yes, probably the vaccine will help. But you know, if I have to wait a little while to see how it works on somebody else, I don’t feel that big a risk,’” Rasmussen said.

The 12% of Utahns who said they are either waiting to see the effects of the vaccine, along with the 14% who are in no particular rush and the 12% who are dead set against getting the shots, offered a variety of reasons, including concern over side effects despite those being minimal.

Recent COVID-19 case decline in Utah is leading to fewer hospitalizations, deaths

Some said they don’t trust the vaccines, citing the speed at which they were developed, while others want to make sure Utahns who are more vulnerable were able to get inoculated first, and a few don’t like what they view as the government telling them what to do.

Centerville resident Mary Ann Kershisnik, 86, said her friends are split over whether to get vaccinated, but she didn’t hesitate when she was offered a vaccine dose late one January night by a nurse who had to use up an opened vial before it spoiled.

“Both sides are definitely part of my circle. Some really thought it was great and some thought it was madness. I don’t know, I felt good about it,” Kershinsnik said, especially after leaders of The Church of Jesus Christ of Latter-day Saints were vaccinated.

“I just believe in vaccines. I’m old enough to have gone through the polio scare,” she said, acknowledging that, unlike her, “a lot of people are fearful.” Although she was feverish and achy for 24 hours after receiving her boost dose of the vaccine last week, Kershinsnik said it wasn’t anything she couldn’t handle.

“It’s wonderful to have some hope that this is not going to go on forever. I think it’s been a terrible year,” she said, describing how her family was unable to gather after losing a granddaughter to cancer. “I guess I just have trust that they wouldn’t give us something that would be harmful.”

Hinckley Institute of Politics Director Jason Perry said there’s been “a substantial step forward” since a previous poll last fall found that just over half of Utahns would take a federally approved vaccine if it became available, with nearly a quarter saying they would refuse it.

Poll: Only half of Utahns say they’d take FDA-approved COVID-19 vaccine

“It is clear that we are on the right track,” Perry said, given that number has dropped to 12%, while 60% of Utahns now say they’ve either gotten vaccinated or want to as soon as possible. “It’s because we have more people in the state who know someone who has received the vaccine without significant side effects.”

Utah health experts have said at least 70% to 80% of residents would have to get the vaccine before changes could be considered to public health measures such as the statewide mask mandate that everyone is expected to follow, including those who have been vaccinated since it’s not clear whether they can transmit the virus.

Only 9% of Utahns said they believe vaccines are being distributed by the state unfairly, citing a number of reasons ranging from frustration signing up for appointments to Utahns with underlying medical conditions not yet being eligible.

“That is a high mark of confidence from voters in the state of Utah and it shows our elected officials have hit this one right,” Perry said.

Utah’s vaccine eligibility list started with front-line hospital workers and has been expanded to include other health care workers, first responders, emergency services personnel, long-term care facility residents and staffs, K-12 teachers and school staffs, as well as now, Utahns 65 and older.

Gov. Spencer Cox had planned to drop the age requirement from 70 to 65 on March 1, the same time that Utahns with specified medical conditions are scheduled to become eligible for the vaccine, but announced Thursday more older residents could start getting the shots immediately.

Utahns 65 and older can now get COVID-19 vaccine, governor says

Cox has stuck to his goal of getting the vaccine to every Utah adult who wants it by the end of May.

Those decisions, sparked by the Biden administration’s purchase of 200 million additional doses and the promise of new vaccines soon being approved for use in the United States, have helped ease some of the initial concerns about the possibility of people “jumping the line” for vaccines, Perry said.

“There is a general sense in our community that not just the process is fair, but you will be able to get the vaccine when it is your turn,” he said. “The fact that it has been benchmarked to age takes the politics out of it as well. It is one of those clear markers.”

Rasmussen said the high number of Utahns who see the system as fair surprised him.

“Getting 80% to agree on anything in America today is hard,” the pollster said. But as Utah’s allotment of doses increases, it’s easier for Utahns to envision a time when there is more than enough supply to meet demand.

And that, Rasmussen said, “takes the edge off a lot of things.”