Washington (CNN) President Donald Trump on Tuesday predicted the coronavirus is "going to go away" despite warnings from Democrats that his White House is asleep amid cresting fears in Washington that the outbreak could spark a pandemic.

The President maintained his sunny optimism about the virus that is showing signs of spreading around the world from its Chinese epicenter and is already having a huge impact on global commerce.

"I think that's a problem that's going to go away," Trump said during a trip to India, expressing confidence that the epidemic will not seriously harm the global economy.

But behind the scenes the President is less calm , and he is expressing frustration at some of the ways his administration is responding to the outbreak, sources familiar with the conversations told CNN. His mood reflects a growing realization among Trump's staff that the coronavirus is going to pose a greater challenge than previously understood.

After weeks of telling Americans that China has a lid on the situation, the President will return from India amid growing concern in Washington over the virus and partisan criticism of his attitude.

A panicked 1,000-point Wall Street sell-off, a building world supply-chain crunch and a looming hit to global growth together could pose peril for Trump by slowing the strong economy he plans to ride to reelection.

But even more worryingly, the virus is spreading to Europe and the Middle East in a way that has experts warning it could soon become a full-blown pandemic. In such a scenario, the US could not expect to escape from a wave of infections and Trump would face a test of his leadership and capacity to bring a jumpy nation together.

Trump acknowledged Monday's Wall Street plunge, but noted futures were higher ahead of Tuesday's market open in the United States and he said that his administration was putting "a lot of talent, brainpower" behind tackling the virus.

The President ticked though administration efforts to contain the virus, claiming the US had "essentially closed the borders."

"We're watching very carefully," Trump said. "We're fortunate so far and we think it's going to remain that way."

But Democrats are now sounding the alarm, with Senate Minority Leader Chuck Schumer charging Monday that the President is "asleep at the wheel" as the threat builds.

A serious outbreak in the US could put a health system already facing a tough flu season under severe pressure, posing an organizational challenge for an administration that habitually stokes chaos and sends mixed messages.

Speaking to reporters on Tuesday, Dr. Nancy Messonnier of the Centers for Disease Control and Prevention said it's too soon to tell whether the problem will go away, as the President suggested.

"We're going to be, again, preparing as if this is going to continue, preparing as if we're going to see community spread in the near-term. But I'm always going to be hopeful that disease will decline either for the summer, or that we'll be over-prepared and that we won't see this kind of high levels of transmission here in the US," she said.

Trump could face a leadership test

Even if worst-case scenarios don't come to pass, Trump's so far blasé approach to the virus, assuring Americans that Chinese President Xi Jinping is on top of the epidemic, does not seem sustainable for much longer. The President has also confidently predicted that warming spring weather could snuff out coronavirus , despite no evidence that is the case.

Yet as disquiet mounted by the hour in Washington, Trump was still not showing much concern late Monday about a virus that has infected more than 80,000 people and killed at least 2,704 worldwide and has now popped up in South Korea, Iran, Italy, Afghanistan, Kuwait and elsewhere.

During a visit to India, the President sent a tweet suggesting all was well, and predicted the stock market would bounce back.

"The coronavirus is very much under control in the USA. We are in contact with everyone and all relevant countries. CDC & World Health have been working hard and very smart. Stock Market starting to look very good to me!" Trump tweeted.

The President was technically correct. Coronavirus cases here have been linked to Americans returning home from China or Japan, and have yet to spread outside contained areas. But his tone jarred with an increasingly ominous mood back home.

In a sign of increasing urgency, the administration gave senators a classified briefing on Tuesday morning about coronavirus contingency plans. Officials from the CDC, Department of Health and Human Services, the Department of Homeland Security, the National Institutes of Health and the State Department took part.

Lawmakers leaving the briefing Tuesday said that officials told them that a vaccine is at least one year to 18 months away.

"The vaccine for the Coronavirus is moving more rapidly than any vaccine we have already tried to approve -- but it will take a year or 18 months," said retiring Republican Sen. Lamar Alexander, who chairs the Health, Education, Labor, and Pensions Committee. "The way to stop (an outbreak) is quarantine and monitoring."

He added, "I believe it's under control. Do I think it will spread in the United States? The advice we got today is inevitably it will spread."

The White House, meanwhile, asked Congress for $1.25 billion in emergency funding to combat the outbreak.

"The Administration believes additional Federal resources are necessary to take steps to prepare for a potential worsening of the situation in the United States," it said in a letter sent to Capitol Hill.

In a statement, House Speaker Nancy Pelosi blasted the emergency funding request as "long overdue and completely inadequate to the scale of this emergency." She hinted that her chamber would provide more resources than Trump requested.

"The House will swiftly advance a strong, strategic funding package that fully addresses the scale and seriousness of this public health crisis," Pelosi said.

Schumer had slammed Trump earlier Monday, saying the President was not taking the situation sufficiently seriously.

"All of the warning lights are flashing bright red. We are staring down a potential pandemic and the administration has no plan," the New York Democrat warned.

"The Trump administration has been asleep at the wheel. President Trump, good morning, there is a pandemic of coronavirus. Where are you?"

After the administration's funding request was unveiled, Schumer criticized it as "too little, too late."

Privately, Trump has lashed out against decisions made by his team and insisted stricter controls be put in place to prevent those with coronavirus -- even Americans -- from entering the United States, the sources told CNN

As The Washington Post first reported , Trump was upset to learn that 14 Americans who tested positive for coronavirus were allowed to fly back to the United States after spending weeks in quarantine on a cruise ship in Japan. He was initially told they would remain in Asia for further quarantine and was frustrated he wasn't kept abreast of the decision-making to allow them to return to the US.

He complained to multiple White House officials last week that he hadn't been consulted on the decision. But by Tuesday he seemed to agree it was ultimately the right call.

But Chelsea Clinton, who teaches at the Mailman School of Public Health at Columbia University, said the President was ignorant about global health and presided over an administration that had sought to cut funding in the area.

"The Trump administration is chronically inept at, and seemingly uninterested in, any type of long-term planning," Clinton wrote in an opinion piece on CNN.com

But White House counselor Kellyanne Conway insisted in an interview with Fox News that Trump had taken "very robust action" working with local and state officials for weeks.

"The President has been so fully engaged on the issue from the beginning," she said, citing daily calls, policy meetings and restrictions on travelers entering the US from China.

Growing concern on Capitol Hill

Republican Sen. Richard Shelby of Alabama, meanwhile, said he was certain the administration could cope if the situation worsens.

"Staring all of us in the face is the specter of a possible pandemic and something we haven't witnessed in my lifetime," Shelby told reporters on Monday.

But the chair of the Senate Appropriations Committee said of Trump's team: "We have to depend on them. I depend on them. Give them a chance."

The sudden upsurge in political heat over the coronavirus in Washington came after Mike Ryan, executive director of the World Health Organization's Health Emergencies Program, said that while the virus was not yet a pandemic, it was time to prepare for it to evolve in such a way.

"Look what's happened in China: We've seen a significant drop in cases, huge pressure placed on the virus and a sequential decrease in the number of cases; that goes against the logic of pandemic. Yet we see in contrast of that, an acceleration of cases in places like Korea, and therefore we are still in the balance," he said.

Economic fears mount

The global stocks sell-off on Monday came amid fears among investors that far from waning, the coronavirus outbreak was escalating in a way that could cause genuine economic damage.

The Dow closed 1,032 points, or 3.6%, lower, registering its worst day in two years.

The slump on Wall Street knocked out all the gains made by stocks so far this year, raising the possibility that the losses could extend beyond a one-day panic.

"This is how corrections start," Art Hogan, chief market strategist at National Securities, told CNN International's Zain Asher.

"I think what is really happening, this is a market that fell into a bit of complacency about the fact that this coronavirus was largely contained in China and China was doing a lot about it," Hogan said.

The losses in the US followed steep dives in Asia and Europe on Monday as investors take in the risks to corporate profits and economic growth posed by the coronavirus' spread.

The warning signs have been building for days, and may just have reached a critical mass on Monday.

Apple, for instance, said last week that the outbreak was hurting its business more than it had previously expected and was hampering its manufacturing and sales in China.

Manufacturers in technology, transport and other sectors in the United States and across the world are reliant on supply chains fanning out from China, and a lengthy disruption could pose problems for sustained economic growth.

Since China represents such a large slice of the global economy, any slowdown sparked by efforts to contain the virus could have long-term effects everywhere, even if health experts manage to hold off a pandemic.

Ryan Detrick, senior market strategist for LPL Financial, warned: "The coronavirus might be slowing in mainland China, but the huge jump over the weekend to various other countries has many reassessing 2020 growth estimates."

"The International Monetary Fund already lowered China's growth this year, but should the virus continue to spread to other parts of the world, we could see quickly decreasing earnings and growth outlooks," Detrick said in a statement.

Any sign that the US economy is being affected would surely catch Trump's eye and might jolt him into more urgent action.

The President gets higher marks from voters for his economic management than for any other aspect of his presidency. He incessantly cheers stock markets as they hit new highs. But a growth slowdown and the psychological impact of a prolonged correction could complicate his pitch for a second term.

This story has been updated with additional developments Tuesday.