“Assuming everything stays bipartisan, the main issue remains timing,” one Democratic aide said.

Both Democratic and Republican lawmakers have slammed as insufficient the administration's emergency request for $2.5 billion to counter to outbreak, which asks for just $1.25 billion in new money and would siphon $535 million in federal funding meant to fight Ebola.

“This is bad,” Rep. Tom Cole (R-Okla.), who sits on the House Appropriations Committee, said Wednesday of the coronavirus, “but if we had an Ebola outbreak here in the United States, that would be devastating. So we shouldn’t be penny-wise and pound-foolish here. We need to come up with something different."

Senate Minority Leader Chuck Schumer (D-N.Y.) released a competing funding proposal Wednesday calling for $8.5 billion in emergency money to battle the coronavirus, after previously demanding Tuesday that the administration increase its request to at least $3.1 billion with no cuts to Ebola funding.

House Minority Leader Kevin McCarthy (R-Calif.) said lawmakers were considering a supplemental package closer to $4 billion.

"I think $2 billion is a little low,” McCarthy, a close Trump ally, told reporters during his weekly press conference. “I think we're probably looking at $4 billion in this process, having spoken to Democrat House members from Appropriations.”

Appropriators acknowledged that the final figure may be higher. And House Majority Leader Steny Hoyer (D-Md.) also said Wednesday that Congress may need to pass multiple emergency funding bills over the course of the outbreak.

Dr. Anthony Fauci, the director of the NIH’s National Institute of Allergy and Infectious Diseases, stressed Wednesday that the government must “be prepared for things to happen that are beyond your control,” and suggested a line of messaging for Trump to deliver from the White House.

“The index card would say that at the present time, things are under control here. But realistically, we need to be prepared for the possibility and maybe the likelihood that we will see more cases here. And the degree to which we can contain them will determine the impact on the country,” Fauci said on Fox News in response to a question on what he would like to hear from the president at his news conference. “We have a pandemic preparedness plan. We need to dust it off and get ready to implement it.”

Fauci said that “nothing has changed now” with regard to the coronavirus’ threat to the Americans, and insisted that “the containment of the cases in the United States is really good.” But the increased rates of transmission in other countries “may ultimately have an impact here,” he cautioned.

“When you see, really, transmissions that are multi-generational in places like South Korea, in Italy, in Japan, in Iran, there’s the danger that this will turn into a true pandemic,” he said. “And if it does, we will have to deal with it. We cannot make ourselves be completely excluded from that because pandemics don’t know geographic boundaries.”

The White House this week was weighing whether to appoint a coronavirus czar to coordinate the response to the spreading epidemic, according to two people familiar with the matter.

Trump, in a Wednesday evening press conference, named Vice President Mike Pence to lead the effort combating the spread of the coronavirus. Trump cited Pence's experience as governor of Indiana as qualifying him to spearhead the growing threat of the global outbreak.

Officials this week debated whether such a role was necessary as the global spread increased the urgency to elevate its response, and the Trump White House was eager to appear like it’s in control of containing the virus within the United States. Appointing a czar would mirror the Obama administration’s response to the Ebola outbreak in 2014 when it named Ron Klain, a former adviser to Vice President Joe Biden, to coordinate nationwide efforts to fight that epidemic.

Former Food and Drug Administration commissioner Scott Gottlieb was among a handful of officials being discussed for the role of coronavirus czar. Trump returned from a trip to India early Wednesday morning and quickly announced the evening press conference to discuss the response.

Health and Human Services Secretary Alex Azar has been leading the administration's coronavirus efforts, which have come under fire after the health department botched the rollout of coronavirus lab tests and left hundreds of Americans aboard a quarantined cruise ship where coronavirus rapidly spread. White House officials are worried that a bungled response to the coronavirus could put the economy, stock market and Trump's reelection at risk.

A White House spokesman said the president had no plans to create a czar position. “The President took decisive action by creating the Coronavirus Virus Task Force a month ago and is pleased with the leadership of @SecAzar to protect the public health,” deputy press secretary Judd Deere wrote on Twitter.

At his second appearance this week on Capitol Hill, House lawmakers grilled Azar on the administration's response to the coronavirus outbreak, including the question of why the White House hasn't appointed a czar to oversee an effort that combines public health with international diplomacy.

"I serve as the lead on this," Azar responded, pointing to his role on the president's recently convened task force. "I work on a daily basis with the chief of staff and the president. So if there's any de-conflicting between agencies that needs to happen, it can happen there."

Azar described the Trump administration's coronavirus response as "the smoothest interagency process I’ve ever experienced in 20 years of dealing with public health emergencies," remarking that "the oddity is what the Obama administration chose to do with Ebola. I’m not sure why they felt things weren't working and they needed to do that."

Questioned during the hearing by Rep. Rosa DeLauro (D-Conn.) about POLITICO's reporting regarding White House consideration of a coronavirus czar, Azar replied: "I don't put much stock in anonymous sources in POLITICO."

Azar declined to say whether he discussed the subject of a czar during his conversation with the Trump earlier Wednesday, citing his desire to keep their talks confidential, but added that "the president is the one who said that HHS is the lead agency."

“I don’t anticipate one," Azar said, when asked whether he foresees the eventual appointment of a coronavirus czar. "This is working extremely well. If it doesn’t work or if there’s a change, that’s for the president to decide.”

Following Azar's session with lawmakers Wednesday, DeLauro scolded the secretary for his comments and suggested the president's preoccupation with the state of the economy could influence his deliberation over a potential czar.

"It doesn't pay to be flip in this environment we have today on these issues," she said, adding: "Maybe the president's concern with the Dow is pushing him to think we should have a czar. Who knows what lurks in the heart of the president?"

Oklahoma Rep. Tom Cole, a top Republican on the House Appropriations Committee, expressed some interest in a White House-appointed coronavirus czar, but cautioned against putting someone with a political background in the role.

"I'm not sure I like the idea of bringing in a political guy. If you want to bring in a health care professional, that makes sense," Cole said. "When you're in a war, you listen to your generals, and when you're in a biomedical crisis, you listen to your doctors and scientists."

Earlier Wednesday, Trump accused media outlets of inappropriately stoking panic amid mounting public health concerns over the coronavirus, breaking again with CDC officials who have warned of its threat to the U.S.

Former Food and Drug Administration commissioner Scott Gottlieb is among a handful of officials being discussed for the role of coronavirus czar. | Zach Gibson/Getty Images

Trump announced his plans for his press conference, which was not on his White House schedule when it was released Tuesday night, minutes after arriving back in Washington Wednesday morning.

“Just landed. India was great, trip very successful. Heading to the White House. Meetings and calls scheduled today,” Trump wrote on Twitter 28 minutes after Air Force One touched down at Joint Base Andrews. “@CDCgov, @SecAzar and all doing a great job with respect to Coronavirus! Briefing this afternoon.”

Less than an hour and a half later, the president lashed out at the media, accusing MSNBC and CNN of overreacting to the coronavirus threat and of intentionally spooking economic markets.

“Low Ratings Fake News MSDNC (Comcast) & @CNN are doing everything possible to make the Caronavirus [sic] look as bad as possible, including panicking markets, if possible. Likewise their incompetent Do Nothing Democrat comrades are all talk, no action. USA in great shape! @CDCgov,” Trump wrote.

“I will be having a News Conference at the White House, on this subject, today at 6:00 P.M. CDC representatives, and others, will be there. Thank you!” he added.

The president’s social media posts Wednesday represent the latest discrepancy in administration officials’ assessment of the coronavirus crisis.

Nancy Messonnier, the director of the CDC’s National Center for Immunization and Respiratory Diseases, said Tuesday that a coronavirus outbreak in the U.S. is now inevitable, warning that “it’s not a question of if, but rather a question of when and how many people in this country will have severe illness.”

But later Tuesday, White House National Economic Council Director Larry Kudlow offered a significantly rosier outlook, telling CNBC that, “we have contained this, I won’t say airtight, but pretty close to airtight.”

Trump himself has remained similarly optimistic, seemingly claiming during a Tuesday press conference in India that the U.S. was “very close” to developing a coronavirus vaccine. The White House later said the president was referring to the Ebola vaccine, which the FDA approved two months ago.

Asked Wednesday about the conflicting messages from the White House and the CDC, Anne Schuchat, the agency's principal deputy director, acknowledged that "it can be a confusing time right now," but said "the good news is that here in the United States the virus is contained."

Still, "we need to be prepared in case things change here," Schuchat continued, referencing the numerous outbreaks abroad.

Despite White House efforts to downplay concerns, stock markets have plummeted this week amid escalating fears that the public health emergency could explode into a full-scale pandemic, with U.S. stocks suffering their worst day in two years on Monday. Trump sought to calm the financial instability in a tweet Monday, writing that the coronavirus “is very much under control” in the U.S. and that the “Stock Market [is] starting to look very good to me!”

The president defended the government response again Tuesday, tweeting that the “CDC and my Administration are doing a GREAT job of handling Coronavirus.”

Trump lamented, however, that “no matter how well we do … the Democrats talking point is that we are doing badly” in attempting to thwart the outbreak. “If the virus disappeared tomorrow, they would say we did a really poor, and even incompetent, job. Not fair, but it is what it is,” he wrote.

Caitlin Emma, Jennifer Scholtes, Meridith McGraw and Sarah Ferris contributed to this report.