CHICAGO — A widespread failure in the United States to invest in public health has left local and state health departments struggling to respond to the coronavirus outbreak and ill-prepared to face the swelling crisis ahead.

Many health departments are suffering from budget and staffing cuts that date to the Great Recession and have never been fully restored. Public health departments across the country manage a vast but often invisible portfolio of duties, including educating the public about smoking cessation; fighting opioid addictions; convincing the reluctant to vaccinate their babies; and inspecting restaurants and tattoo parlors.

Now, these bare-bones staffs of medical and administrative workers are trying to answer a sudden rush of demands — taking phone calls from frightened residents, quarantining people who may be infected, and tracing the known contacts and whereabouts of the ill — that accompany a public health crisis few have seen before.

Nationwide, local and state health departments have lost nearly a quarter of their work force since 2008, according to the National Association of County and City Health Officials. As the nation’s local and state public health officials confront a pandemic that has paralyzed much of the world, many of them have made their situation plain: They are heading into a crisis without the resources they need.

“We’ve had to deal with budget cut after budget cut,” said A. Scott Lockard, director of the Kentucky River District Health Department, which serves seven counties in rural eastern Kentucky. “Our staffing level is much less now than what it was previously. People are wearing several different hats and sharing job responsibilities for things that they were not doing before, so we’re already operating at peak efficiency and we have no capacity when something like this happens.”

With the virus now consuming all attention, key functions have been put on hold. Some health departments are now making reductions in home health care and education on unwanted teenage pregnancy and other core issues. In Wayne County, Ohio, the health department called off upcoming seminars to vaccinate people in Amish communities, where parents are often reluctant to immunize their children.

“Local health departments in the state of Ohio are underfunded,” said Nicholas Cascarelli, the commissioner for the Wayne County Health Department in Ohio, near Akron. “We’re kind of quiet and we go about our business. But when stuff like this happens, people notice.”

Since the coronavirus outbreak began, many of the nation’s thousands of health departments have coped by pulling their entire staffs into the effort. For smaller departments, there is little wiggle room.

Cindy Kinnard, the director of public health in Kewaunee County, a mostly rural Wisconsin community on the shore of Lake Michigan, said her 23 years at the department have usually felt short-staffed.

At its height, the department had eight employees. Now it is down to six, hardly enough to handle the flood of tasks in this moment, she said.

“We’re getting a lot of telephone calls and a lot of questions,” she said. “We are definitely understaffed for it.”

On Friday, President Trump declared a national emergency over the coronavirus pandemic, pledged up to $50 billion in aid and appeared to strike a deal with House Democrats to provide other assistance, offering some hope of an injection of resources that could provide temporary relief.

He had previously authorized an $8.3 billion supplemental package for coronavirus issues; state and local health agencies will receive $950 million under the law.

“It’s definitely going to help,” said John Auerbach, president and chief executive of Trust for America’s Health, who suggested that some states could use the funds to attempt to quickly hire more epidemiologists or increase laboratory capacity.

Still, the money comes as local health workers already are fully engulfed in the immediate crisis. And Mr. Auerbach said that the money, which must be spent on coronavirus-related actions, will not solve long-term problems many agencies face. “The money will run out and the core budget will be what remains,” he said.

A panel of experts studying the public health system in the United States, convened by Resolve, a nonprofit public policy group, recently found that the country would need an additional $4.5 billion annual investment to protect national security and “create the conditions in which people can be as healthy as possible.”

And a study by the Trust for America’s Health, a nonprofit public health advocacy group in Washington, found in 2019 that “chronic underfunding has presented a consistent obstacle” to the nation’s public health systems.

“Since 2008, they’ve really been hit hard, and the vast majority of them have not recovered,” said Adriane Casalotti, chief of government and public affairs for the National Association of County and City Health Officials. “That’s apparent in both budgets and also in their work force.”

Mr. Lockard, the director of the public health system in eastern Kentucky, said his department had roughly 300 employees in the early 2000s but was now down to 110 workers.

They were doing what they could, he said. But it was not going to be easy. “It shows that our public health infrastructure has been severely weakened over the years,” he said. “We have much fewer people to respond when we have a situation like this.”

A staff of 30 clinical nurses was now down to eight. His preparedness planner left 14 months ago, he said, because of budget cuts. His sole epidemiologist, he said, was “completely overwhelmed.” The area was still dealing with one of the most intense flu seasons seen in years.

On the federal level, the Centers for Disease Control and Prevention, the nation’s main public health agency, has seen its budget fall 10 percent over the last decade, adjusting for inflation, according to the Trust for America’s Health report. The C.D.C. saw a 2 percent increase in its budget program funding between the 2018 and 2019 fiscal years, after accounting for interagency transfers and one-time funding, and as measured in inflation-adjusted dollars.

And while the report found that total state spending on public health increased 2 percent in the 2018 fiscal year, 17 states and the District of Columbia cut public health funding that year, while 21 percent of local health departments reported reductions in budgets for the 2017 fiscal year.

The federal Public Health Emergency Preparedness program, which helps state and local health departments prepare for and respond to emergencies, including outbreaks of infectious diseases, has also seen funding reductions, falling from $940 million in the 2002 fiscal year to $617 million in the 2019 fiscal year, according to statistics compiled by the Trust for America’s Health.

Some of the states hardest hit by the coronavirus run the gamut in terms of public health emergency preparedness, according to rankings by Trust for America’s Health, with Washington State in a top category of preparedness, California in the middle, and New York in the bottom.

Still, even Washington State’s system has been hampered by a lack of resources needed for upkeep, equipment and the flexibility to respond to emergencies. In recent weeks, state lawmakers there discussed adding $5 million to the budget to aid the state’s coronavirus response. That later rose to $100 million. Then, this week, just as lawmakers were finalizing the budget, they doubled the new funding to $200 million.

Around the country, some public health systems are actually in stronger shape than in years past. Amelia Clark, administrative officer of the Spokane Regional Health District in eastern Washington, said her agency had grown to 263 employees from 221 employees 10 years ago.

“Washington’s done a pretty good job of funding public health,” she said.

Still, the Spokane agency has been contracting with retired public health workers in recent days to help handle what is expected to be a wave of coronavirus cases. By the end of a week in which cases of the virus in the United States rose above 2,100 and schools and offices closed, the stress on local health care systems was already being felt.

A website for the Kentucky Cabinet for Health and Family Services suggests that residents call an 800 number if they are feeling ill “but would not have sought care if not for Covid-19.”

Numerous attempts to call the number on Thursday were met with a busy signal. On Friday, calls went through, and a recording was available offering details on the virus and tips for not contracting it. There was also an option to speak with a health care specialist. One of them picked up after a one-hour hold time.

“The biggest problem off the top is there’s sort of like a surge capacity,” said Dr. Marcus Plescia, chief medical officer for the Association of State and Territorial Health Officials. “This all-hands-on-deck metaphor, of people getting pulled off of all sorts of things to work on this, some of that’s OK. But the problem is you’re pulling across all of these programs, all of which have been cut and chopped away at over the last few years, so there’s not the same capacity as there once was.”

State public health departments, Dr. Plescia said, were staffed with some excellent workers. The issue is that there are not enough of them. Now the coronavirus was going to put the model to the ultimate test. “Everybody’s been saying that this is a problem, that we haven’t been investing in public health, and now we’re seeing how that might play out to be a bigger issue,” he said.

Dr. Boris Lushniak, the dean of the School of Public Health at the University of Maryland, said he was concerned that in the coming weeks and months, the demands on local and state public health workers would become difficult to sustain.

“We can project out what’s going to happen in the next few weeks,” he said. “We are going to get an influx of diagnostics. It’s here, there’s no stopping it, it is spreading person to person. And as the numbers surge up, that puts more pressure on the states and locals.”

On Thursday afternoon, Debra Nagel, a nurse who specializes in communicable disease and preparedness, answered the phone at the Jasper County Health Department in Rensselaer, Ind., and said she would be happy to briefly chat about her department’s response to the coronavirus outbreak.

“I think the main challenge is —” she said, stopped short by another phone trilling in the background.

“I guess I don’t really have the time to talk,” she said. “I’m the only one here.”

She apologized and hung up.

Julie Bosman reported from Chicago, and Richard Fausset from Atlanta. Mike Baker contributed reporting from Seattle.