To federal health officials, asking states on Tuesday to suspend use of the Johnson & Johnson coronavirus vaccine until they can investigate six extremely rare but troubling cases of blood clots was an obvious and perhaps unavoidable move.

But where scientists saw prudence, public health officials saw a delicate trade-off: The blood clotting so far appears to affect just one out of every million people injected with the vaccine, and it is not yet clear if the vaccine is the cause. If highlighting the clotting heightens vaccine hesitancy and bolsters conspiracy theorists, the “pause” in the end could ultimately sicken — and even kill — more people than it saves.

With coronavirus cases spiking in states like Michigan and Minnesota, and worrisome new variants on the horizon, health officials know they are in a race between the virus and the vaccine — and can ill afford any setbacks.

“We are concerned about heightened reservations about the J&J vaccine, but in addition to that, those reservations could spill over into public concerns about other vaccines,” said Dr. Paul Simon, the chief science officer for the Los Angeles County Department of Public Health.

Officials at the Food and Drug Administration and the Centers for Disease Control and Prevention said Tuesday that the break in vaccinations could last only a matter of days as they sort out what happened, determine whether to place limits on the use of the vaccine and examine ways to treat clotting should it occur.

Around the country, people who have taken the one-dose Johnson & Johnson vaccine — and even those who have not — were left to weigh their risks, especially women ages 18 to 48, who accounted for all six cases of blood clots.

The repercussions could be more dramatic than federal officials are bargaining for, just as they were in Europe, where a similar clotting issue has turned the AstraZeneca vaccine into something of a pariah. There, too, officials stressed that blood clotting in people injected with the AstraZeneca vaccine was extremely rare. Yet according to a YouGov poll published last month, 61 percent of the French, 55 percent of Germans and 52 percent of Spaniards consider the AstraZeneca vaccine “unsafe.”

“It’s a messaging nightmare,” said Rachael Piltch-Loeb, an expert in health risk communications at the N.Y.U. School of Global Public Health. But officials had no other ethical option, she added. “To ignore it would be to seed the growing sentiment that public health officials are lying to the public.”

The one-dose Johnson & Johnson vaccine was just beginning to gain traction among doctors and patients after its reputation took a hit from early clinical trials suggesting its protection against the coronavirus was not as strong as competitor vaccines made by Pfizer-BioNTech and Moderna. Before Tuesday’s pause, some patients were asking for it by name.

“I knew that I wanted to get the Johnson & Johnson — the idea of it being one and done really appealed to me,” said Kayli Balin, 22, a freelance web designer and recent graduate of Wellesley College who was scheduled to get the Johnson & Johnson vaccination on Tuesday — only to have her appointment canceled. Now she will get the Moderna vaccine, she said.

But amid the blizzard of news and social media attention around the “pause,” those gains may well be lost, especially if the rare blood clotting feeds politically driven conspiracy theorists and naysayers, who seemed to be losing ground as the rate of vaccinations ramped up.

“This is exactly the wrong situation at the wrong time at the very moment that Republicans are reconsidering their hesitancy,” said Frank Luntz, an American pollster who studies messaging for Republicans, a group that has exhibited high levels of skepticism about the coronavirus vaccines.

Brian Castrucci, an epidemiologist and head of the de Beaumont Foundation, which studies public health attitudes, said: “It’s an easy turn to, ‘If they kept this from us, what else have they kept from us?’ We need to get out in front of this very quickly. ”

The problem is getting the public to understand relative risk, said Rupali J. Limaye, who studies public health messaging at the Johns Hopkins Bloomberg School of Public Health. She noted that the potential rate of blood clotting in reaction to the vaccine is much smaller than the blood clotting rate for cigarette smokers and for women who use hormonal contraception, although the types of blood clots differ.

Dr. Angela Rasmussen, a virologist with the Center for Global Health Science and Security at Georgetown University, made that point Tuesday on Twitter, noting the incidence of blood clots among those vaccinated, those taking oral contraceptives and those who have Covid-19.

Patients interviewed on Tuesday said the news gave them pause — if not for themselves, then for what it would mean for the nation’s ability to slow the spread of the virus. Jen Osterheldt, 33, of Norwalk, Ohio, who is pregnant and received the Johnson & Johnson vaccine about a month ago, said she would take it again, but worried that others would shun it even if the pause was lifted.