Why is it so hard to find a COVID-19 test? Sites are short-staffed, and rapid supply is low.

Coronavirus testing sites have few openings and rapid tests are nearly impossible to find as the omicron surge sends testing demand higher than the system can bear and thousands of people a day seek to find out whether they’ve been infected.

Not a single PCR or rapid test appointment was available between Tuesday and Saturday at 40 CVS locations from Philadelphia to Folsom, according to the company’s online appointment scheduler. There were also no test appointments available until next week at Rite Aids in Philadelphia and its suburbs.

No Delaware County-run testing sites had online appointments available in the coming days, and Montgomery County officials said theirs had been fully booked this week and last. In Philadelphia, up to 1% of city residents are being tested per day, signaling high demand, but even with more testing becoming available, “it still won’t be enough,” the health commissioner said Wednesday.

“I was really worried, more than anything, that we wouldn’t be able to find a test,” said Wren Allen, whose family started feeling sick over the weekend and couldn’t find testing appointments near their Blue Bell home sooner than a week away. The family tested positive after a friend gave her rapid tests, she said Wednesday as she isolated at home and nursed a scratchy throat.

As the skyrocketing number of coronavirus infections has broken records here and nationwide, the strain on the testing system has increased. The very transmissible omicron variant, combined with still-circulating delta, has pushed some hospitals to their brink and spurred the highest demand for testing since the emergence of delta.

New Jersey, which had the nation’s second-highest case rate per capita, was averaging more than 29,000 new cases per day on Wednesday. Pennsylvania’s seven-day average was above 20,000 cases a day, according to federal data analyzed by the New York Times.

Each of the tens of thousands of cases represents a positive PCR test and an appointment or clinic somebody had to get to. And on top of those numbers are all the people who have swabbed their noses at home — clearing rapid tests from store shelves.

Officials say the number of people infected with the virus is being drastically underestimated, either because people can’t find an appointment, their results are delayed, or they’re using at-home tests that go unreported.

Without a well-established federal testing infrastructure, some stopgap efforts were being implemented around the region to bring a measure of relief: The Federal Emergency Management Agency will open a five-day-a-week testing site at Cibotti Recreation Center in Southwest Philadelphia, city officials announced Wednesday, and opened one near Newark last week.

The Pennsylvania Department of Health opened a drive-through site at Mercy Fitzgerald Hospital in Delaware County on Monday, and the county opened two additional sites. Montgomery County is adding 6,000 appointments at its public clinics this month. Local governments were working to purchase rapid tests.

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But the main thing preventing more testing appointments from being available, several doctors and officials who work with sites around the region said, is a lack of staff. With an existing shortage of health-care workers and, now, an increasing number calling out sick with COVID-19, sites don’t have extra hands to administer more tests.

“It was just a frustrating process,” said Nick Ambolino, 27, who waited three hours for a COVID-19 test at a Montgomery County urgent care on New Year’s Day after being possibly exposed to the virus. “You can’t help but think, ‘We’ve been living with this thing for two years and don’t have a robust testing infrastructure in place, government-sponsored or private.’”

People often start lining up for Sayre Health Center’s testing site in West Philadelphia around 7 a.m., an hour and a half before it opens. Three days a week, its staff have been testing 600 to 700 people a day — the same number it did when open five days a week during the fall.

“People wait hours for a test. We can only test so many people, so people get a little bit upset when the line cuts off right in front of them or we have to take lunch,” said Jill Gansert, a doctor at Sayre. “It’s been a real challenge.”

Like at Sayre, some local testing sites remain open for walk-ins or have available appointments. But in many places, demand has been exceeding supply.

The Pennsylvania Department of Health plans to open other new testing sites and to provide free rapid testing in certain areas, but a spokesperson provided no details about when or where those resources would become available.

Philadelphia is working on a large order of at-home rapid tests and will be helped by the new FEMA site, but Health Commissioner Cheryl Bettigole cautioned that availability will remain limited. Officials in Delaware and Chester Counties said they have seen a dramatic increase in demand. Montgomery County administered more than 18,000 tests in December at its five county-run sites, more than double the number in November, said public health administrator Christina Miller.

Staffing “more than anything else” limits the number of people who can be tested, said Montgomery County medical director Richard Lorraine — something that sites across the state and region are struggling with.

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“All the things that we were short of when the pandemic began — supplies for testing, primarily — we pretty much have that fixed now, but now it’s a matter of staffing,” said Gerald Maloney, chief medical officer for hospital services at Montour County-based Geisinger Health. “Now we just don’t have the people to administer the tests.”

People getting tested at Sayre, where preregistration is not required, have often told the staff that they couldn’t find appointments elsewhere or struck out searching for rapid tests.

“I feel very lucky that we are able to offer the services, but people are frustrated,” Gansert said. “Every time you walk outside, someone asks about testing.”

When people can’t find a testing appointment, more join the race to snatch up difficult-to-find rapid tests in pharmacies or online, which aren’t counted in official data. Increasingly, people who can’t easily find a test are not getting tested at all. Along with the use of at-home tests, that contributes to the undercounting of infections.

But forgoing a test and simply isolating is the right move, officials say, for people who have symptoms or exposure and can’t find a test.

In the days before Christmas, Stephen Skilton, 38, spent hours on the route between Fishtown and Medford, Burlington County, stopping at more than a dozen pharmacies in hopes of snagging a rapid test before seeing relatives, including his 93-year-old grandfather. He came up short.

“I didn’t expect everything everywhere to be out,” he said.

On Wednesday, he prepared for another drugstore expedition, this time for his girlfriend, who may have been exposed. Now, he said, they won’t venture farther than their neighborhood — but are prepared to stay home if they get sick.

Staff writer Laura McCrystal contributed to this article.