(CNN) — Early clues — in places like New York, California and Seattle — indicate social distancing may be slowing the rate at which coronavirus cases otherwise would have increased in the United States.

But health officials warn it’s too early to know how well it’s working — and even if mitigation measures continue, the number of US deaths still could be hard to take.

“We’re starting to see glimmers … just the inklings” that the daily increases in US cases aren’t as steep as they would have been without social distancing, Dr. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, told CNN on Tuesday morning.

“We’re not seeing (a turnaround) yet,” he said.

Cases and deaths still are soaring: At least 3,300 people have died in the US — more than 570 of which were reported on Monday alone. More than 171,000 coronavirus cases have been reported in the country.

There are, however, signs that rates of case increases may have been slowed in some places. It’s too early to pinpoint why, though the signs have come after federal and state officials urged people to stay at home or avoid crowds:

• New York has by far the most US cases (75,700+) and deaths (1,500+). But the state’s average of day-over-day case increases for the last seven days was 17%, compared to 58% for the previous seven-day period, a CNN analysis shows.

• In Northern California, “the surge we have been anticipating has not yet come,” Dr. Jahan Fahimi, medical director at the University of California San Francisco Health, told CNN. San Francisco issued the country’s first shelter-in-place order two weeks ago, and officials hope it is paying off. That hope has not necessarily reached Los Angeles County, where hospitals are seeing a steady patient increase.

• In Washington state’s King County, two new reports from an institute that specializes in studying disease transmission dynamics showed social distancing measures appeared to be making a difference.

Still, even if social distancing is maintained through May, some 82,000 people in the US could die from coronavirus by August, a University of Washington model shows.

The model estimates that more than 2,000 people could die each day in the United States in mid-April, when the virus is predicted to hit the country hardest.

Dr. Deborah Birx, the White House’s coronavirus response coordinator, has said worst-case projections show “between 1.6 million and 2.2 million deaths if you do nothing.”

Doctors and health officials still are pleading for people to stay home, to slow the disease’s spread and dampen the rush at hospitals in hot spot cities, where physicians are running low on supplies to protect themselves and equipment to support patients.

“We don’t have a magic bullet (treatment) for this disease, so the best thing we can do is prevent infection,” and therefore we must continue to generally stay at home, Dr. Rochelle Walensky, chief of infectious disease at Massachusetts General Hospital, told CNN Tuesday.

New Orleans hospitals may run out of ventilators by the weekend, Collin Arnold, director of the New Orleans Office of Homeland Security and Emergency Preparedness, told CNN.

“Staying at home and isolating is the way to beat this,” he said Tuesday.

Your coronavirus questions, answered

Economic consequences

Signs continue to emerge that the pandemic is posing huge challenges to the US economy.

Food banks across the nation are struggling. Millions of newly unemployed people mean the food banks are seeing a flood of new clients, just as supplies start to dwindle because of growing demand from consumers stuck at home.

The investment bank Goldman Sachs, meanwhile, predicts the unemployment rate rising to 15% by the middle of the year.

‘Stay at home, buy us time’

In parts of the country, walking into work feels like walking into a war zone for many medical care workers.

“There is not enough of anything,” one trauma physician at Miami’s Jackson Memorial Hospital said. “There are just so many patients who are so sick, it seems impossible to keep up with the demand.”

Inside New York City’s Elmhurst hospital, one doctor told CNN “we are at the brink of not being able to care for patients.”

It may seem simple, another doctor says, but staying at home could also be saving those working to save patients.

“It feels like coronavirus is everywhere and it feels like we have very little to protect ourselves from getting very sick ourselves as healthcare workers” Dr. Cornelia Griggs, a Pediatric Surgery Fellow at Columbia University said Monday. “I want everyone at home to know that even though it seems like staying at home is futile, it’s not.”

“We need everyone at home to hold the line, stay at home. Buy us time, flatten the curve.”

States clamp down

More than two dozen governors have stepped up to combat the spread of the virus, issuing stay-at-home orders that now cover more than three-fourths of the American population — and authorities have begun cracking down on those who refuse to abide.

In Kentucky, Gov. Andy Beshear also issued an executive order Monday barring residents from traveling to other states — with just a handful of exceptions — and directing those who are returning to Kentucky from another state to self-quarantine for two weeks.

“Right now we have more cases in other states,” he said. “What it means is your likelihood of getting infected and potentially bringing back the coronavirus may be greater in other states than ours. You need to be home anyways.”

In North Dakota, residents coming back from any of the 24 states the US Centers of Disease Control and Prevention have classified as having “widespread disease” are also required to quarantine for two weeks. Those states include California, New York, Illinois and Georgia.

President Donald Trump extended guidelines on social distancing for another month but said a nationwide stay-at-home order was still unlikely.

Repercussions for those not staying in

Those not following orders to stay at home and keep a distance have begun facing consequences.

A popular Florida pastor was arrested Monday for continuing to hold large services and charged with unlawful assembly and violation of public health emergency rules, both second-degree misdemeanors.

“Last night I made a decision to seek an arrest warrant for the pastor of a local church who intentionally, and repeatedly, chose to disregard the orders set in place by our president, our governor, the CDC and the Hillsborough County Emergency policy group,” Hillsborough County Sheriff Chad Chronister said.

“His reckless disregard for human life put hundreds of people in his congregation at risk, and thousands of residents who may interact with them this week in danger,” he added.

In New Orleans, police issued arrest warrants for a man who organized a funeral second line over the weekend and also cited the band leader.

Police said that more than 100 people participated and the organizer refused to stop the second line when asked by police.

That person’s family reached out to the mayor’s office and apologized this week.

“I heard from the family. They reached out yesterday. They sent their apologies. That it will never happen again. It has really sent a message to our community throughout,” New Orleans Mayor LaToya Cantrell told CNN. “Our musician community, our cultural bearers have stepped up and said, hey, no more in the city of New Orleans. This is — this is very serious here.”

The-CNN-Wire

™ & © 2020 Cable News Network, Inc., a WarnerMedia Company. All rights reserved.