When President Trump announced new travel restrictions on Europe in a prime-time Oval Office address Wednesday, many national-security experts, including some who worked in his White House, declared the move probably would do little to contain the spread of the novel coronavirus already confirmed in 44 states and the District of Columbia.

When he floated a payroll-tax cut to juice the economy as stock markets plummeted, many financial analysts said it would not be enough help for the hourly workers hit hardest by the slowdowns in major industries and the low-income families burdened by the closings of schools.

And as he has repeatedly sought to play down the threat of the virus — calling it “very, very low” in his Wednesday address and emphasizing that the United States has fewer cases than other nations — Trump has gone against the warnings of his administration’s medical experts, who have bluntly stated that the numbers are likely to grow significantly.

Trump’s response to the global pandemic has represented the most serious crisis of his presidency, one with widespread ramifications for public safety, national prosperity and his own reelection chances. But the solutions his White House has proposed have in many cases fallen short of what experts say has shown promise in China and South Korea, raising alarms that the nation has lost crucial time in meeting the challenge.

The spread of the virus has also left Trump vulnerable to political attacks from rivals such as leading Democratic presidential candidate Joe Biden, who laid out his own plans Thursday and said “the virus laid bare the severe shortcomings of the current administration.”

Trump aides have countered that the administration has mounted a robust, all-of-government response to a massive international crisis that has caught the world by surprise. Production of testing kits has been ramped up after initial missteps, and officials have convened roundtables to consult key stakeholders, including tourism and service industry executives, private health insurance providers and banking executives.

During a meeting Thursday with Irish Prime Minister Leo Varadkar at the White House, Trump said the administration was considering invoking emergency powers under the Stafford Act that could allow federal officials to tap more resources.

“The United States, because of what I did and what the administration did with China, we have 32 deaths at this point,” Trump said, referring to an earlier move limiting flights from China, where the novel coronavirus originated. “Other countries that are smaller countries have many, many deaths. Thirty-two is a lot. Thirty-two is too many. But when you look at the kind of numbers that you’re seeing coming out of other countries, it’s pretty amazing when you think of it.”

By Thursday night, the number of deaths had climbed to 41.

But for Trump, the rapid spread of the illness in the United States since those early steps with China has undermined his chief talking point that he has handled the outbreak with decisive action. More than 1,600 cases have been confirmed in the United States since then, and the numbers are expected to spike further as testing ramps up.

The president’s biggest initiative this week — the ban on foreigners coming to the United States from 26 European countries — was one that World Health Organization officials and other leading health experts have warned against, saying it complicates a coordinated global response.

Such bans can cause people to keep their travel surreptitious, making it harder to do crucial contact-tracing of the infected, experts say. It also can choke the supply chain of health workers, expertise and medical supplies. Travel bans, experts also point out, can caused friction, hampering information-sharing and international efforts — as has happened between the United States and China at a time when coordination and transparency has been crucial to fighting the virus.

“It’s entirely unwise. First of all, it violates WHO recommendations and treaties that the U.S. has signed on to. But it doesn’t even do anything to impact the epidemic,” said Lawrence Gostin, a global health law professor at Georgetown University. “Many of the countries in Europe besides Italy have just as many cases or less than the United States. The idea this would reduce transmission here is not based on evidence. The reality is germs don’t respect borders.”

One federal official involved in the response, speaking on the condition of anonymity to avoid angering others in the administration, said the travel ban on Europe was too late and should have been done at the end of February, when cases began surging in Italy.

Tom Bossert, who served as Trump’s homeland security adviser, credited the president for a “positive step” in sounding the urgency of the threat during his prime-time address Wednesday. But Bossert, in a tweet, called the travel restrictions of “little value” and a “Poor use of time and energy.” He predicted that in two weeks the administration might “regret wasting time.”

Another former administration official echoed those thoughts in an interview, saying the White House should have been making sure hospitals had adequate resources and guidelines to make sure they had enough bed space and capacity for an influx of patients.

“They should have a standard playbook on what they should be recommending,” said the former official, who spoke on the condition of anonymity to talk frankly about the administration’s response. “They’re making this up as they go.”

That also seemed true in the case of the White House’s other big remedy this week, a proposed payroll-tax cut that the president boasted would offer the public “substantial relief” — a move he hoped would bolster investor confidence to stabilize the free-falling stock market.

In a rare appearance in the White House briefing room Tuesday, Trump told reporters he would present his plan the following day to Republican senators. Employing his flair for showmanship, Trump called the tax cut “a big number,” “very major” and “very dramatic.”

But Democrats, and some Republicans, have rejected the idea, and some economists have said its impact in stemming losses for ordinary workers amid the coronavirus scare would be applied unevenly and be less effectual than other options.

Brookings Institution fellow Jay Shambaugh said a payroll-tax cut would help higher-wage earners more than lower-income workers and that it would mete out assistance slowly rather than deliver a shorter-term economic jolt that could bolster investor confidence.

“What would really help give the markets confidence would be a policy response that is dealing with the public health issues, as well as dealing with the economic issues,” said Shambaugh, who served on the White House Council of Economic Advisers in the Obama administration. He called for more money to go to states, which are on the front lines of responding to the crisis, as well as strengthening social safety nets and sending direct payments to the public to boost consumer confidence.

On top of the administration’s policy struggles, the president has overseen a disjointed public messaging operation.

Trump initially put Health and Human Services Secretary Alex Azar in charge of an interagency coronavirus task force. But weeks into the crisis, he moved to install Vice President Pence as the leader in a bid to exert more White House control.

That has led to conflicting public guidance and the muzzling of key medical experts. Officials at the Centers for Disease Control and Prevention hold media briefings twice a week, but those often are delayed to allow the White House coronavirus task force to make its own remarks first. Trump has often overridden others with his own remarks; the president announced three policies during his Oval Office address that contained errors and were later cleaned up by his aides.

Trump’s insistence early in the crisis that the virus was being contained gave Americans a false sense of security, said Jeanne Marrazzo, director of the division of infectious diseases at the University of Alabama at Birmingham.

“When you have the chief executive and the vice president who clearly say things that are not only scientifically inaccurate, but operationally inaccurate, that everybody can be tested, it’s no wonder people are confused and they get a false sense of security,” Marrazzo said. She pointed to Pence’s announcement March 3 touting a new policy allowing “any American” to be tested for the novel coronavirus with a doctor’s order. That has created tremendous confusion among doctors and clinicians at hospitals.

To some observers, the chaotic messaging has been perhaps the most damaging response of all. One HHS official, speaking on the condition of anonymity to discuss the matter frankly, noted that when the coronavirus task force has its daily briefings, the officials are huddled close together in the White House briefing room — a visual image that Trump sees as a show of force but one that conflicts with the CDC’s guidance on social distancing to limit the spread of the illness.

“They would all be considered close contacts if one of them was actually sick,” the official said.

Yasmeen Abutaleb and Jeff Stein contributed to this report.