WASHINGTON — The federal government’s program to expedite the shipping of valuable protective equipment to coronavirus hot spots has left hospitals that are out of the spotlight struggling to secure their own protective gear as they watch the outbreak creep closer.

The Trump administration has repeatedly endorsed the Federal Emergency Management Agency’s system of flying masks, respirators, gloves, goggles and surgical gowns from overseas suppliers to the United States. The new “air bridge” is rushing supplies to the most hard-hit areas within days instead of weeks.

But officials who represent areas with fewer serious infections say the system has left them to navigate a mind-boggling private marketplace where state officials and hospital leaders face backlogged orders, last-minute cancellations and rising costs. And the coronavirus can hit fast, like the outbreak that has erupted in South Dakota.

“I don’t take anything away from hot spots,” Gov. Steve Bullock of Montana, a Democrat, said in an interview. “But we don’t want to become one of them.”

The federal government’s approach has forced local officials to get creative. Some have enlisted 3-D printing. Others have turned to car or painting shops to make medical gear for emergency workers.

Dr. Thomas Tobin, the chief medical officer at the community hospital in Grand Junction, Colo., is not facing the challenges of an area like New York City. The medical facilities he oversees have 10 patients on ventilators. But with just 30 days’ worth of protective gear for his hospital workers, he said he was desperate for assistance now rather than when infections soar.

“It’s like not getting a smoke alarm until after the fire’s already in your house,” Dr. Tobin said. “It’s a little late at that point.”

The Trump administration’s system of procurement has also prompted criticism from members of Congress and governors who say shipments of previously ordered personal protective equipment, or P.P.E., confirmed for other hospitals are being commandeered and redirected to hot spots around the United States. The leaders of the House Homeland Security and Oversight Committees wrote a letter to Peter T. Gaynor, the FEMA administrator, saying that “the agency’s opaque and evolving processes are clearly not meeting the needs that communities have right now for P.P.E. and medical supplies.”

Democrats have also criticized the involvement of Jared Kushner, President Trump’s son-in-law, as a back channel for the politically well-connected who make direct contact with Mr. Trump. Mr. Kushner said at a recent White House briefing that he ensured N95 masks were delivered to a New York City public hospital after Mr. Trump told him that “he was hearing from friends of his in New York that the New York public hospital system was running low on critical supply.”

“That’s not how the system should work,” said Juliette N. Kayyem, a former assistant secretary at the Department of Homeland Security. “You want to align supply with need. The random phone call is not necessarily need.”

Administration officials say the more than 40 flights that have delivered protective equipment are just one way to fulfill the needs of localities. In exchange for expediting the shipments of the protective equipment, FEMA requires the distributors to sell about half of the remaining supplies to 100 counties deemed to be struggling the most based on government data on the number of hospitalized patients, number of deaths from the outbreak and available hospital space.

The rest of the supplies from the flights are sold to distributors’ pre-existing customers, forcing many counties to scramble.

MaryAnn E. Tierney, one of FEMA’s regional administrators, said she had fielded numerous calls from leaders of counties that were not in the Top 100 list. But Ms. Tierney said in an interview that air bridge flights supplied just a portion of available protective gear.

The Defense Department has also distributed 11 million N95 masks, and FEMA is encouraging communities to clean and reuse protective gear. The Department of Health and Human Services has also awarded contracts to five companies to produce 600 million respirator masks over the next 18 months.

The administration’s Supply Chain Stabilization Task Force is also working to procure additional protective gear from 11 different manufacturers, according to a FEMA spokesman.

Ms. Tierney said the counties could still turn to private distributors that bring equipment on large cargo ships or from the companies involved in the air bridge program that are free to sell about half of the shipments.

“If you’re not in a hot spot, there are still supplies being computed into the system because 50 percent of what lands on one of those planes is going to different locations throughout the country,” she said.

For many communities, that is not nearly enough.

The inspector general for the Department of Health and Human Services released a report this month showing widespread shortages of protective gear at hospitals. In Montana, Mr. Bullock said two-thirds of the state’s hospitals reported receiving shipments of supplies that were less than what they had ordered or the shipments were outright canceled.

The state has received 78,000 N95 masks from the federal government, a sliver of the 550,000 Mr. Bullock said the hospitals needed. Without federal assistance, the state government has been forced to enter a new market and has faced increasing competition from other states and hospitals. Mr. Bullock recently had to ask North Dakota for 50,000 masks.

“It leaves us at the bottom of the bucket,” Mr. Bullock said of the distribution system.

Dr. Scott Ellner, the chief executive of Billings Clinic, a health care system in Montana, said the system did receive materials from the federal government, but “that has really slowed to a trickle at this point.”

“We are aware that equipment is now being diverted to other hot spots,” he said.

Dr. Ellner’s staff has been forced to solicit public schools, dentists’ offices and universities for 3-D printers to make additional masks. A ski company produced molds for thousands of masks, and a fishing company made gowns for hospital workers.

“There’s a point where you can only reuse your equipment so much to where it’s not necessarily doing what it’s supposed to be doing,” Dr. Ellner said. “It’s not preventing the spread but creating risk, not just for hospital workers but for transmissions to other patients in the hospital.”

Dr. Lisa Moreno, a professor of emergency medicine at the Louisiana State University Health Sciences Center in New Orleans, said she had gained hope that infection rates in her devastated region had plateaued. But she added that when she was not working in an emergency room, she had faced “astronomical” costs for protective gear in the private market.

And her physicians did not have the resources to know which vendors were scammers and which companies sold flawed or fraudulent materials, distinctions she said she thought the federal government was better suited to make.

Dr. Moreno, the president-elect of the American Academy of Emergency Medicine, said she was also worried for colleagues who could experience new outbreaks in the weeks to come.

“I don’t want them to go through what I’ve had to go through, where we are having to wash down our gowns with antiseptic hand wipes and having to wear the same N95 for five shifts,” Dr. Moreno said. “And you have to take it off to take a drink of water, and you don’t know where it put it down because you don’t know what’s contaminated.”