WASHINGTON — The nation’s coronavirus testing capacity, already straining to keep up with demand, is facing enormous new pressure, with holiday travelers waiting in long lines to be tested, overworked laboratories struggling to keep up and rapid at-home diagnostics flying off pharmacy shelves as the Omicron variant fuels a rapid spike in Covid-19 cases.

Two years into the pandemic, the surging desire for tests in the face of limited supply threatens to thwart President Biden’s response, but it is hardly a new problem. The United States has bungled testing from the outset of the pandemic, experts say, and matching supply with demand has been a persistent challenge for both the Trump and Biden administrations.

Mr. Biden came into office vowing to make testing for the virus cheap and easily accessible, and there have been some improvements since he was sworn in. Laboratory tests are more plentiful now, and more than a dozen at-home tests are available, up from zero in January. The Food and Drug Administration has sped up its approval process, and the supply of at-home tests has increased steadily since August; last month, it was expected to double by March.

But the United States remains a far cry from Europe, where more than three dozen types of at-home tests are available for as little as $1 to $2 per test. Americans can pay as much as $25 for a box of two, and Mr. Biden’s plan to have insurers reimburse for those purchases will not take effect until mid-January at the earliest.

In Miami, cars lined up bumper to bumper this week at a drive-through test site. In Providence, R.I., there were no testing appointments available at a local CVS; those looking to be tested were instructed to buy over-the-counter at-home tests.

In Brooklyn, people waited in line for two hours on Thursday to be tested at a medical clinic in Park Slope. New York State, an early epicenter of the pandemic, recorded 21,027 positive coronavirus cases on Friday, the highest number reported on a single day during the entire pandemic.

Around the country, retailers — both online and brick-and-mortar — are having trouble keeping over-the-counter tests in stock. Walmart was selling Abbott’s rapid antigen test online Friday, but many stores in Washington, D.C., and its Maryland and Virginia suburbs were sold out. In Houston, the pharmacist at a local Walgreens, Hanh Ho, said shipments of at-home tests arrive every Wednesday and sell out the same day.

“They’re a hot item,” Mr. Ho said. “One guy came in and took all of them.”

The difference between the United States and Europe is rooted partly in their differing health care systems, but also stems from a critical decision that the Biden administration made months ago: not to subsidize tests in the same way it subsidizes vaccines. Some Western countries decided early on to shoulder much, if not all, of the testing costs, guaranteeing demand and, some argue, lowering prices through purchasing agreements with major manufacturers.

The Biden White House only recently — in back-to-back announcements in September and October — committed to spending a total of $3 billion to buy tests. More than half has been spent on over-the-counter tests, senior administration officials said.

“It’s been a dreadful situation from Day 1 of the pandemic, and I would say it’s still botched,” said Eric Topol, a professor of molecular medicine at Scripps Research. “We should have an ample supply of rapid tests freely available,” as in Britain, Israel and some other countries, he added.

Earlier this month, Mr. Biden announced that at-home tests would be reimbursed by insurers for the 150 million Americans who have private insurance, and that the administration would distribute an additional 25 million tests to community health centers and rural clinics, which tend to treat lower-income patients.

But the announcement drew immediate complaints from public health experts, including Dr. Topol, who objected to requiring that people go through the process of seeking reimbursement. Dr. Topol said the notion that consumers would routinely front such costs in the hope of reimbursement was “a nonstarter.”

White House officials say they are working to further expand production of at-home tests, which would in turn create market competition and, presumably, drive down the cost. Demand is only expected to grow after the Centers for Disease Control and Prevention endorsed a new approach on Friday for allowing children exposed to the coronavirus to stay in school, testing at least twice over the course of a week, instead of requiring them to quarantine.

“We are continuing to do everything we can to continue to grow that supply,” Carole Johnson, the testing coordinator for the White House coronavirus response team, said in an interview Friday.

During any infectious disease outbreak, there are two major reasons to use tests, experts say: to determine if someone is infected, and to protect others from getting infected. To diagnose Covid, doctors generally rely on polymerase chain reaction, or P.C.R., tests — highly sensitive tests that are performed in laboratories.

But with Omicron spreading quickly, experts foresee a jump in demand for rapid antigen tests, the quick version that are sold over the counter, which many people use for peace of mind.

During a White House briefing on Friday, Dr. Rochelle Walensky, the C.D.C. director, advised people to “do a test and make sure that you’re negative before you mix and gather in different households” over the holidays, “for that extra reassurance.”

Reassurance is what Stan Smith, 67, was seeking Friday at a busy testing site in Orlando, Fla. He said he had no symptoms and was vaccinated, yet he had already waited nearly 90 minutes for a test.

“We’ve got to look out for each other,” he said. “I don’t know if I’m going to be around anybody who could contaminate me, but I don’t want to be that person either. Christmas is only a week away.”

Mara Aspinall, an expert in biomedical diagnostics at Arizona State University who keeps track of testing capacity, has forecast that in January, the United States will produce a total of 613 million coronavirus tests, including 243 million rapid antigen tests, the ones sold over the counter.

“If Omicron continues to spread as fast as it appears, we’ll be very challenged on any reasonable number of tests, particularly prophylactic testing before gathering,” she said, “and that is a huge concern.”

Test manufacturers report that demand is booming — even for the most expensive tests.

Executives at Detect recently received authorization from the F.D.A. to market a new type of molecular at-home test, which its developers say is as sensitive — but not nearly as expensive — as P.C.R. tests, generally considered the gold standard for detecting coronavirus infection. Their work was financed by the National Institutes of Health.

The price is high: $49 per test, plus $39 for a reusable “hub,” which is used to run the tests. But when Detect began selling the tests online this week, demand was so high that company officials said they will more than likely start reducing the number of test kits that someone can order from four to two.

“We haven’t done any advertising of any sort,” the company’s chief executive, Hugo Barra, said in an interview Friday. He said the company intends to scale up production so the cost of the tests falls.

Dr. Ezekiel Emanuel, a bioethicist at the University of Pennsylvania who advised Mr. Biden during his transition, said the administration should simply purchase over-the-counter tests and distribute them to pharmacies, where they could be sold at a low cost or even given away.

“If you had central purchase by the government, you could drive the price way down, which is very important,” he said.

For now, the high cost of at-home tests is a huge barrier; in some states, including Massachusetts and Colorado, officials are distributing them free of charge. Yet some consumers have expressed unease about the at-home tests, fearing that they are not as reliable as P.C.R. tests.

“I would be more comfortable leaving it to professionals rather than myself,” said Fortune Maduba, 23, a grocery store worker in Houston who was preparing to travel to Nigeria.

In Providence on Friday, Silvi Goldstein, 28 and a graduate student at the University of Rhode Island, was waiting to be tested at a state-run site outside the Rhode Island Convention Center. Staff members at the testing site said labs were overwhelmed, and Ms. Goldstein said she expected to wait 72 hours for her results — three times as long as she had to wait during the summer.

“I’ve considered at-home tests — they’re expensive,” Ms. Goldstein said.

According to a report this month by the Coronavirus Resource Center at Johns Hopkins University, the United States has both the world’s highest rate of tests per capita and the worst Covid-19 outbreak. The worse the outbreak, the more tests are needed, the center said, but experts disagree about what rate of testing is sufficient.

The rate of testing varies significantly from state to state, and not always in tandem with the coronavirus threat. For instance, Massachusetts’ rate of testing is about three times that of Michigan, even though Michigan’s rate of positive tests is three times that of Massachusetts. Demand for testing dropped in many places after vaccination became widely available.

“We got it up and running and then everyone sort of eased off because of the vaccine and said, ‘We’re not really going to need this stuff,’” Dr. Emanuel said. “And the problem is, that’s not true.”

Reporting was contributed by Maria Jimenez Moya from Houston, Ben Berke from Providence, R.I., Eric Adelson from Orlando, Fla., and Grace Gorenflo from Seattle.