WASHINGTON — President Donald Trump on Wednesday named Vice President Mike Pence to coordinate the government’s response to the coronavirus, even as he repeatedly played down the danger to the United States of a widespread domestic outbreak.

Trump’s announcement, at a White House news conference, followed mounting bipartisan criticism that the administration’s response has been sluggish and came after two days of contradictory messages about the virus, which has infected more than 81,000 people globally, killing nearly 3,000.

“The risk to the American people remains very low,” Trump said, flanked by top health officials from several government agencies. “We have the greatest experts, really in the world, right here.”

The president said he would accept whatever amount of money congressional Democrats wanted to give for the virus response, adding, “We’re ready to adapt and we’re ready to do whatever we have to as the disease spreads, if it spreads.”

“We’ll spend whatever is appropriate,” he said.

Several top health care experts at the news conference echoed Trump’s optimism but also offered a more sober assessment of the future risks. Dr. Anne Schuchat, principal deputy director of the Centers for Disease Control and Prevention, warned Americans that there would be more infections.

“Our aggressive containment strategy here in the United States has been working and is responsible for the low levels of cases that we have so far. However, we do expect more cases,” she said as Trump stood behind her. “The trajectory of what we’re looking at over the weeks and months ahead is very uncertain.”

About a half-hour later, Trump contradicted Schuchat’s assessment, telling reporters that “I don’t think it’s inevitable.” He left the door open to travel restrictions beyond China, to other hard-hit countries such as South Korea and Italy, and said his early decision to stop flights from China had held the virus at bay.

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But the CDC confirmed minutes later that a new infection in California was contracted by a person who did not appear to have traveled to countries hard hit by the virus or been exposed to a known coronavirus patient. That raised the prospect that the virus was spreading through unknown means.

Health experts have questioned the CDC’s decision to limit testing for the virus to people who have traveled in China or have come into contact with someone who has. Other countries are testing more broadly for the coronavirus among people from countries where outbreaks have been growing, including Italy, Iran and South Korea.

“We’re testing everybody that we need to test,” Trump insisted, “and we’re finding very little problem, very little problem.”

Earlier in the day, Trump had accused journalists of making the situation “look as bad as possible” even as government health experts warned that the coronavirus threat in the United States is only beginning. Without offering any details on transmission, Alex Azar, the health and human services secretary, confirmed the new case on Wednesday afternoon, bringing to 60 the total number of infections that have been counted in the United States. Azar said that health officials were still figuring out how the new person became infected.

The politics of coronavirus shifted drastically Tuesday when Dr. Nancy Messonnier, director of the CDC’s National Center for Immunization and Respiratory Diseases, told reporters that “it’s not so much of a question of if this will happen anymore but rather more of a question of exactly when this will happen.” She said that hospitals and schools should begin preparing for an outbreak, and that she had even spoken to her own family about “significant disruption of our lives.”

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Trump sought Wednesday to counter that message with a much less dire one, holding up a Johns Hopkins University study that he said showed the United States as the most prepared country in the world to confront a virus. He said he was “amazed” that tens of thousands of people died from the flu each year, contrasting that number with the several dozen currently infected with coronavirus.

“We’re very, very ready for this, for anything, whether it’s going to be a breakout of larger proportions or whether or not we’re, you know, we’re at that very low level,” Trump said.

The president, who is a well-known germophobe, urged Americans to be vigilant about covering their coughs and washing their hands, and he told the story of a man who recently came up to him and hugged him.

“I said are you well? He says no,” Trump said. “He said, ‘I have the worst fever, and the worst flu.’ He’s hugging and kissing me. I said, ‘Excuse me,’ I went and started washing my hands.”

Trump has been reluctant to give in to what he considers an “alarmist” view about the virus, an administration official said. The president has repeatedly said that, like the flu, the new coronavirus will dissipate with warmer, more humid weather, even though officials have warned him that relatively little is known about the virus, and it may not behave as others do.

Economists see growing recession risk as coronavirus spreads

The possibility of the virus spreading in the United States comes as the administration grapples with budget cuts and personnel moves that critics say have weakened the system for dealing with such health crises. The White House in 2018 eliminated a dedicated position on the National Security Council to coordinate pandemic response, the same year that the Trump administration narrowed its epidemiological work to 10 countries from 49.

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In November, a task force at the Center for Strategic and International Studies, which included five current and former Republican senators and House members, warned that “the United States remains woefully ill prepared to respond to global health security threats” and recommended the reinstatement of an NSC coordinator and a recommitment of funding and attention to global health programs.

Instead, the president’s budget request this month for the fiscal year that begins in October would cut the CDC’s budget by almost 16%, and the Health and Human Services Department’s by almost 10%. The proposal’s $3 billion in cuts to global health programs included a 53% cut to the World Health Organization and a 75% cut to the Pan American Health Organization.

And his naming of Pence as his point person immediately drew partisan fire even as he vowed to ensure that the “full resources of the American government” were deployed to protect Americans from the coronavirus.

The Democratic National Committee immediately pointed out that as governor of Indiana, Pence was blamed for aggravating a severe AIDS outbreak among intravenous drug users in a rural Indiana county when he opposed calls for a clean needle exchange program on the grounds it would encourage more drug use.

It has fallen to Azar to make the case that the government is up to the task of containing the virus as anxiety grew around the world about vulnerability to a still-mysterious affliction that does not respect international borders.

New cases popped up across Europe, dozens of infections in Iran raised fears of an unbridled spread through the Middle East, and the first confirmed case was reported in Latin America — a Brazilian man who had returned from Italy just as Brazil is in the midst of its Carnival celebrations.

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For the first time, more new cases were reported outside China — where the outbreak began two months ago — than inside, according to figures from the World Health Organization.

Chinese authorities cautioned that the falling infection rate might be only temporary, while South Korean officials scrambled to contain the largest outbreak of cases outside China — including a U.S. soldier deployed in South Korea. Across the United States, universities began bringing students home from abroad and canceling overseas study programs.

Trump has privately expressed frustration to numerous officials about his administration’s efforts confront the virus, according to someone familiar with his comments.

As recently as last weekend, the president grew furious that he had been sidelined from a decision to return some Americans infected with the virus to the United States, and he made his anger to Azar known. Officials in the White House have since wrestled with how best to present Trump with information during a fast-moving situation, one aide said.

The White House’s muscular internal messaging efforts kicked in Wednesday. Supporters were pelted with multiple emails assuring them that Trump was overseeing an “aggressive coronavirus response,” and that the “full weight of the U.S. government” was working to safeguard Americans from illness, according to one message.

Trump’s attempts to calm the American public have also occasionally been laced with a degree of alarm, with Trump telling reporters at a news conference in India on Tuesday that “there’s a very good chance you’re not going to die.”

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Some of Trump’s political allies tried to question the motivation of some of his top health officials for warning the public about the spread of the virus. Rush Limbaugh, the conservative talk radio host, on Wednesday argued without foundation that Messonnier was being purposely alarmist to undermine Trump because she is the sister of Rod Rosenstein, the former deputy attorney general who was a frequent target of Trump’s ire.

“In that town, I’m telling you, everything is incestuous. Most of that town is establishment-oriented or -rooted, which means they despise Trump,” Limbaugh said on his show.

Trump’s reassurances to the public appear at least in part aimed at calming global markets. On Tuesday, a day after its worst one-day slide in two years, the S&P 500 closed down 3%. The S&P 500 ended Wednesday down about 0.4%, bringing its losses for the week to more than 6%.

Moody’s Analytics predicted a 40% chance that the virus would grow into a global pandemic that would push the United States and the world into a recession. On Wednesday, Trump said he believed that “the stock market will recover. The economy is very strong.”

For a second day, Azar was on Capitol Hill on Wednesday defending his work, telling lawmakers that he was overseeing “the smoothest interagency process I’ve experienced in my 20 years of dealing with public health emergencies.”

Azar said that the CDC had already exhausted the $105 million rapid response fund that the federal government had been using in its initial response efforts. He has proposed shifting $136 million from other health programs to the coronavirus to replenish the government’s efforts.

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A day earlier, he told a Senate panel that medical supplies were badly needed for the nation’s emergency stockpile, including 300 million masks for health care workers alone.

But Wednesday, he faced bipartisan concern about the administration’s $2.5 billion request.

Lawmakers from both parties have said the White House request is far short of what is needed and relies on the transfer of existing funds — including $535 million intended to counter the spread of the Ebola virus.

“These cuts are shameful,” Rep. Anna G. Eshoo, D-Calif., said Wednesday evening at a separate House hearing with Azar.

Sen. Chuck Schumer of New York, the Democratic leader, proposed on Wednesday to increase the president’s emergency request drastically, to $8.5 billion in new funds, including $3 billion for a public health emergency fund, $1.5 billion for the CDC, $1 billion for vaccine development and $2 billion for reimbursing states and cities for efforts they have so far made to monitor and prepare for potential cases of the virus.

Trump said he would gladly accept the additional funds.

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