RICHMOND — Tiffany Smith tilted her head way back, sending her long ponytail almost to her waist and allowing a nurse to stick a cotton swab up one nostril, then another.

“Oh, damn!” she said, wiping her nose after undergoing a free coronavirus test in an east Richmond parking lot. “Whoo!”

Though she hated how it felt, Smith, 47, had been seeking the nasal swab since she and her husband, Charles, started having fevers, coughs, sweats and headaches about a week ago. Smith works at an assisted-living facility, where a co-worker caught the novel coronavirus. She and Charles, a self-employed barber, are uninsured, and the cost of tests at a private clinic was too steep.

“Patient First was talking, like, $90,” said Smith, who worries that if she and Charles have the virus, their five children could be next. One has been running a fever.

The Smiths got their tests Tuesday at Eastlawn Shopping Center, a forlorn plaza anchored by a shuttered Food Circus. Next door sits Creighton Court, a troubled public housing complex that the city would like to demolish.

But on this day, with dozens of medical personnel and volunteers decked out in masks, face shields and bright gowns, the site offered free testing to help control the spread of the pandemic — in a city where 13 out of 14 coronavirus fatalities have been African Americans, and a state where testing has lagged most of the nation.

“In order for us to eventually start easing the [business and social] restrictions, we’ve got to be able to test,” Gov. Ralph Northam (D) said at the testing site. “It is very important to let all Virginians — whatever neighborhood they come from, or whatever walk of life — know that we’re here for them.”

Virginia ranks near the bottom of U.S. states and territories in the number of coronavirus tests administered per capita: 82,753 tests as of Tuesday, or about 9,700 tests per 1 million residents.

That’s on par with Guam, Texas, Kansas and Arizona, according to the Covid Tracking Project. Neighboring Maryland, by contrast, has conducted nearly 18,000 tests per million residents, according to the tracking project and Census Bureau data. New York, with the nation’s worst outbreak, has conducted more than 41,000 tests per million residents.

House Minority Leader Todd Gilbert (R-Shenandoah) seized on the issue Tuesday, demanding that the Democratic governor explain the lag in testing. The Republican Party of Virginia followed up Wednesday, with party chair Jack Wilson saying in an emailed statement that Northam “needs to answer for his failure to lead Virginia through this crisis.”

Virginia officials have said a number of factors contribute to the low rate of testing, which they are striving to improve. Initial shortages of testing supplies nationwide led to strict guidelines for who could be tested — people showing symptoms, over age 65, in a group home or in a vulnerable line of work, such as first responders. The state says it has loosened those restrictions, but many doctors and test providers appear to still have them in place.

In addition, Virginia has vast rural regions with sparse populations where covid-19, the disease caused by the coronavirus, has been slow to spread.

“The Governor then said we lacked the swabs and other testing materials. Yet other states have managed to obtain these resources. Something is fundamentally different — and possibly wrong — with the way Virginia’s testing is being handled,” Gilbert said in a statement. “Virginians deserve answers, and they deserve them now.”

Last week, Northam appointed a task force to expand testing and announced a goal of reaching 10,000 tests per day, up from the 2,600 tests per day that Virginia has been averaging. Northam also said numbers were up to 4,000 a day already.

Despite the testing lags, Virginia’s per capita covid-19 deaths have been far lower than in Maryland. The commonwealth, with a population of 8.6 million, had reported 498 deaths as of Tuesday — fewer than half the 1,023 fatalities suffered in Maryland, population 6 million.

“I think the governor’s been doing a very good job,” House Speaker Eileen Filler-Corn (D-Fairfax) said. “It’s important that a leader, a governor, in the midst of a crisis, is somebody who’s thoughtful, sincere, whose response is based on data, facts and science, and somebody who’s very communicative. And I think he’s doing exactly all that.”

The free testing program in Richmond — conducted in two neighborhoods last week and planned for three more by the end of this one — is too limited to help Virginia catch up on its own. A maximum of 100 people could get tested Tuesday.

But the program could be a first step toward overcoming the financial hurdles and fear that have hindered testing among the hardest-hit population — low-income African Americans.

Lawrence Washington traveled from Richmond’s north side for the test Tuesday, despite a warning from his boss that the service could be a “Tuskegee”-type trap, referring to a notorious and deceptive federal syphilis study on black men in the 20th century.

“My boss, she was talking about, ‘Aargh! I ain’t going to get tested. I remember when they did the Tuskegee experiment. They was shooting people up with syphilis,’ ” Washington, a 47-year-old construction worker, said moments after his test. “I said, ‘Well, they ain’t doing nothing but putting a cotton swab up the nose.’ ”

Washington live-streamed his test, urging friends and family watching to follow his lead. He lives with relatives who have asthma, heart disease and high blood pressure — all risk factors for covid-19 complications.

“This is the makeup of our household . . . which is true of every African American household,” he said.

Richmond Mayor Levar Stoney (D) urged residents not to be deterred by “myths” about testing, stressing that the procedure does not involve “an injection.”

“Please show up. Please show up. We’re begging you to,” he said. “It’s the only way that we get a handle on where the coronavirus is throughout our community.”

Conducted by nurses with help from Virginia Medical Reserve Corps volunteers, the testing was offered to people who lack private health insurance and either have symptoms of the virus, have been exposed to it or have underlying health conditions such as high blood pressure or obesity that could make the virus more lethal.

In a low-income Richmond neighborhood where testing was launched last week, 17 percent of residents who showed up turned out to be positive, said Richmond Health Director Danny Avula. At another, two out of 22 had the virus.

“It’s like shadow boxing,” Stoney said. “We know that the enemy is in the room. We just don’t know where the enemy is.”

Sylvia Seaborne, 61, arrived at the testing site with a fever, a cough and a headache. She wondered whether she could have been infected by an aunt, an assisted-living resident who has tested positive. The retired ­special-education teacher had felt ill for two weeks but could not get a doctor’s office to test her.

“I try to push on, to keep going,” she said.

Wayne Thorpe, 70, a retired firefighter with a nagging cough, also showed up — concerned about his health and that of the brother he lives with, who is on dialysis.

“At least I would know for sure,” he said. “And that’s the main thing, so there won’t be no guessing.”