(CNN) -- The United States reached yet another worrying milestone Sunday as the number of coronavirus cases topped 30,000.
About half of those cases -- 15,168 -- were in New York state, where Gov. Andrew Cuomo said Sunday morning that an estimated 40% to 80% of residents could get the coronavirus over the course of the pandemic.
"All we're trying to do is slow the spread, but it will spread. It is that contagious," he said, adding most people will overcome the illness unless they're older or have an underlying condition.
Dr. James Phillips, a CNN medical analyst and assistant professor of emergency medicine at The George Washington University, agrees with Cuomo's assessment of the virus' potential to spread, he told CNN's Wolf Blitzer on Sunday.
"We've actually been concerned about that on a countrywide level for months," Phillips said. "We've discussed this, we've seen the modeling, we know how these diseases spread and a lot of it depends on our own responsibility and social distancing."
There were at least 31,289 confirmed cases in the United States by Sunday afternoon. At least 395 people have died.
Some states recommend restricting testing
Officials in hard-hit places such as New York and California are warning that panicked people are flooding hospitals for tests and health care facilities will run out of crucial items. The focus has shifted to avoiding broad testing to conserve rapidly dwindling resources such as masks, ventilators and intensive care beds.
Authorities have recommended health care providers avoid testing patients except in cases in which results would significantly change the course of treatment.
New York City health officials issued guidance asking medical facilities to stop testing non-hospitalized patients in an effort to preserve medical supplies, while California Gov. Gavin Newsom said testing should prioritize hospitalized patients, people with compromised immune systems, health care workers, seniors and other high-risk patients.
At a new drive-up testing facility in Miami, Florida Gov. Ron DeSantis said health care workers and first responders would receive priority testing. Anyone ages 65 and older will also be tested, he said.
Millions under restriction
Millions of people in a growing number of states face orders by their governors aimed at keeping them home to prevent further spread of the coronavirus.
Ohio Gov. Mike DeWine on Sunday announced a statewide "stay home" order, requiring residents to stay in with the exception of "essential activities." The order will go into effect Monday night at 11:59 p.m., the governor said, and remain in place until at least April 6, when officials will reevaluate the order.
Businesses deemed "essential" will be allowed to stay open, and restaurants will still be allowed to serve customers via takeout.
Louisiana Gov. John Bel Edwards also issued a "stay at home" order Sunday afternoon, effective Monday at 5 p.m. The order will expire the night of April 12, when the governor plans to reevaluate the situation.
"This order is not something I take lightly," the governor said in a news release, "but it is necessary to protect the health, safety and well-being of our people, our communities and our way of life."
Another "stay at home" order followed in Delaware on Sunday evening. Gov. John Carneey's office said the order would go into effect at 8 a.m. Tuesday and last until at least May 15, or "until the public health threat is eliminated."
Similar measures have been announced in California, New York, Illinois, Connecticut and New Jersey, which have urged nonessential workers to stay home in an effort to prevent the spread of the virus and reduce stress on the health care system.
Each state provides for certain exceptions, such as visiting grocery stories, pharmacies or health care facilities, among others.
"We know the virus spreads through person-to-person contact," New Jersey Gov. Phil Murphy said. "The best way to prevent further exposure is to limit our public interactions to only the most essential purposes."
"Every state will head this way," CNN national security analyst Juliette Kayyem said. "People need to prepare themselves that this gets harder before this gets easier."
Officials press younger people to heed warnings
California Gov. Newsom urged younger residents to avoid visiting beaches as Californians adjusted to their new normal. "(It's) time to recognize it's not only about the old folks, it's about your impact in their lives. Don't be selfish," he said.
New York's Cuomo has repeatedly urged younger people to comply with social distancing. Of the more than 15,000 confirmed cases in New York state, 53% are people between ages 18 and 49, he said.
Nearly 10,000 cases were in New York City. The governor was there Saturday, he said, and took issue with what he saw.
"You would think there was nothing going on in parts of New York City," he said in a news conference Sunday. "You would think it was just a bright, sunny Saturday."
"This is just a mistake," he added. "It's insensitive, it's arrogant, it's self-destructive, it's disrespectful to other people and it has to stop and it has to stop now."
Later Sunday afternoon, Mayor Bill de Blasio said he and the governor were "fully aligned" on the issue and said with regards to parks and grocery stores that New Yorkers should "get what you need" and "get back inside."
"We're not going to be draconian," de Blasio said. "We're going to give people a chance to get used to this. But I guarantee you, we will enforce this new reality."
Cases climb as more people are tested
Numbers have soared as testing has become more available, and among the new cases was Sen. Rand Paul of Kentucky, according to his Twitter account.
"He is feeling fine and is in quarantine," a tweet said. "He is asymptomatic and was tested out of an abundance of caution due to his extensive travel and events. He was not aware of any direct contact with an infected person."
More than 195,000 Americans have been tested, Vice President Mike Pence told reporters Saturday. That total does not include county hospitals or health care labs, the vice president said.
As the demand for tests grows, private companies are joining the government's efforts to restock masks, ventilators and other supplies. The US Food and Drug Administration authorized the use of the first rapid diagnostic test that could detect the disease in approximately 45 minutes. The tests will start shipping this week, according to the California-based manufacturer.
Supply shortages threaten response
As the virus tightens its grip, health care workers and state leaders have sounded the alarm on medical supplies beginning to run short, while some medical experts are going a step further and mentioning staff shortages.
Gov. JB Pritzker of Illinois on Sunday likened the struggle to obtain medical supplies to a "Wild West," telling CNN's Jake Tapper there needed to be more federal coordination.
"We're all competing against each other. We're competing against other countries," Pritzker said on "State of the Union." "You know, it's a Wild West, I would say, out there. And indeed, we're overpaying, I would say, for (personal protective equipment) because of that competition."
"This should have been a coordinated effort by the federal government," he added.
President Trump later addressed Pritzker's remarks on Twitter, saying states "shouldn't be blaming the Federal Government for their own shortcomings. We are there to back you up should you fail, and always will be!"
Supply shortages could also contribute to the coronavirus spreading among health care professionals, Dr. Megan Ranney, an emergency physician with Lifespan, a Rhode Island health system affiliated with Brown University, told CNN's Wolf Blitzer.
"Unless we increase the number of masks and gowns available," she said, "it's a matter of time before most frontline health care workers are infected."
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