The week is set to end with the opening salvos in what is expected to be a bitter fight in Congress over a $3 trillion dollar relief package, including billions for states drowning in debt.

In the days between, it was clear that the struggle against the virus was still raging and that the “moment” was unlikely to pass anytime soon.

He said Americans would face “the darkest winter in modern history” if the administration did not move quickly to formulate a coherent national strategy.

The slowdown has been rippling beyond the early shutdowns in retail and hospitality to professional business services, manufacturing and health care.

The White House, threatening to veto the relief package, said the legislation proposed by Democrats in the House of Representatives was more concerned with “delivering on longstanding partisan and ideological wish lists than with enhancing the ability of our nation to deal with the public health and economic challenges we face.”

President Trump has attacked Democratic governors, accusing them of mismanaging their finances, and he charged that the party’s members in Congress “want help — bailouts — and, you know, bailouts are very tough. And they happen to be Democrat states.”

“The Republican states are in strong shape,” he said last month. “I don’t know — is that luck or is that talent?”

Economists surveyed by Bloomberg expect the report to show that sales fell 12 percent, even more than the 8.4 percent drop in March. That would add up to the worst two-month decline on record.

In an executive order issued late Thursday night, Gov. Andrew M. Cuomo of New York extended the statewide stay-at-home order until June 13 for the regions, including New York City, that do not meet the standards to begin reopening.

Mr. Cuomo had earlier said that Central New York, a five-county area that includes Syracuse, had joined four other upstate regions where some nonessential businesses — including construction, manufacturing and curbside retail — could restart after meeting the seven criteria set by the state.

For New York City to reopen safely and ensure the virus is not spreading out of control, testing and contact tracing are paramount.

But contact tracing has emerged as a contentious point in recent days after Mayor Bill de Blasio shifted control over that effort from the city’s health department to the city’s public hospital system. A New York Times investigation into that decision revealed that as Mr. de Blasio was resisting calls in March to cancel large gatherings and slow the spread of the coronavirus in New York City, he found behind-the-scenes support from a trusted voice: the head of that public hospital system, Dr. Mitchell Katz.

There was “no proof that closures will help stop the spread,” Dr. Katz wrote in an email to the mayor’s closest aides. Dr. Katz said he believed that banning large events would hurt the economy and sow fear. “If it is not safe to go to a conference, why is it safe to go to the hospital or ride in the subway?” he wrote. And, he added, many New Yorkers were going to get infected anyway.

“We have to accept that unless a vaccine is rapidly developed, large numbers of people will get infected,” he wrote. “The good thing is greater than 99 percent will recover without harm. Once people recover they will have immunity. The immunity will protect the herd.”

For Mr. de Blasio, the arguments in Dr. Katz’s March 10 email, obtained by The New York Times, appeared to hold sway over the calls for greater restrictions on daily life from other top officials, who were alarmed by public health surveillance data pointing toward a looming outbreak.

In an unusual public notice, the agency said that early data suggested the Abbott ID Now test, hailed as a rapid means of diagnosing infection with the virus, may return false negatives in patients who actually are infected.

“This test can still be used and can correctly identify many positive cases in minutes,” said Dr. Tim Stenzel, director of the F.D.A.’s Office of In Vitro Diagnostics and Radiological Health.

But negative results should be confirmed with another high-sensitivity test, he said.

The product, which was given emergency authorization by the F.D.A. in late March, has been enthusiastically promoted by President Trump — it was even used as a prop during at least one news conference. Mr. Trump has said the tests are “highly accurate.”

The agency’s warning follows a study by researchers at N.Y.U. Langone Health that found the test could miss infections up to 48 percent of the time.

The F.D.A. also said it had received 15 so-called “adverse event reports” about Abbott’s device, suggesting some users were receiving false negatives. The agency said it was continuing to evaluate the test.

In a statement to investors on Thursday night, Abbott defended the ID Now test, calling it reliable when used as intended. “Negative test results should be considered in the context of a patient’s recent exposures, history and the presence of clinical signs and symptoms consistent with Covid-19,” the statement said.

If the negative results are inconsistent with signs and symptoms, Abbott said, patients should be given an alternative test.

In Wisconsin, residents woke up to a state of confusion on Thursday after the conservative majority on the State Supreme Court sided with the Republican majority in the Legislature on Wednesday night, overturning a statewide stay-at-home order by Gov. Tony Evers, a Democrat.

Across Wisconsin, the court ruling left some residents in a festive mood, heading directly to one of the state’s many taverns to celebrate. Others were determined to stay home, worried that it was too soon to return to crowded restaurants and shops.

“You have the one group that’s like, ‘Yay!’” said Patty Schachtner, a Democratic state senator from western Wisconsin. “And the other group is like, ‘Man, life just got complicated.’”

It was an unsettling microcosm of a country increasingly unable to separate bitter political divisions from plans to battle a deadly disease. Democratic governors in Michigan, Pennsylvania and Wisconsin, backed by public health experts, have urged caution before reopening. Republican legislatures in the states have pushed in the opposite direction, citing economic necessity and personal freedom.

The research, published on Wednesday in the Proceedings of the National Academy of Sciences, could help explain how people with mild or no symptoms may infect others in close quarters such as offices, nursing homes, cruise ships and other confined spaces.

The study’s experimental conditions would need to be replicated in more real-world circumstances, and researchers still do not know how much virus has to be transmitted from one person to another to cause infection. But its findings strengthen the case for wearing masks and taking other precautions to reduce the spread of the virus.

Many people, cooped up inside to slow the spread of the virus, are living in small spaces and reeling from financial worries. Children are home from school in every state.

That has led to another spiraling crisis: Doctors and advocates for victims are seeing signs of an increase in violence at home. They are hearing accounts of people lashing out, particularly at women and children.

“No one can leave,” said Kim Foxx, the chief prosecutor in Chicago. “You’re literally mandating that people who probably should not be together in the same space stay.”

In Chicago, the number of people seeking help has increased significantly in recent weeks. During the first week of March, 383 people called a domestic violence hotline in the city. By the end of April, the weekly number had soared to 549.

“The pandemic has put the pressure on,” said Amanda Pyron, the executive director of the Network, an advocacy organization in Chicago. “No one can go stay somewhere for a few days, have family come over, have the kids go stay with grandparents. Those safety supports aren’t accessible in a meaningful way.”

The American health care system for years has supplied many hospitals with a clear playbook for turning a profit: Provide surgeries, scans and other well-reimbursed services to privately insured patients, whose plans pay higher prices than public programs like Medicare and Medicaid.

“Health care has always been viewed as recession-proof, but it’s not pandemic-proof,” said Dr. David Blumenthal, president of the Commonwealth Fund, a health research organization. “The level of economic impact, plus the fear of coronavirus, will have a more dramatic impact than any event we’ve seen the health care system weather in my lifetime.”

It may ultimately leave Americans with less access to medical care, according to financial analysts, health economists and policy experts. “There is a huge threat to our capability to provide basic services,” Dr. Blumenthal said.

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Industrial production surged last month in China, according to data released on Friday.

Reporting was contributed by Mary Williams Walsh, Katie Thomas, Knvul Sheikh, Marc Santora, William K. Rashbaum, J. David Goodman, Jeffrey C. Mays, Joseph Goldstein, Karen Barrow, Julie Bosman, Kay Nolan, Campbell Robertson, Sheila Kaplan, Sheryl Gay Stolberg, Sarah Kliff, Tariro Mzezewa.

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