"Americans need cash now," Mnuchin said during a White House press briefing on the administration's latest efforts to combat the disease. "I mean now in the next two weeks."

Potentially $250 billion of the package could go toward making direct payments to Americans, a White House official told The Wall Street Journal on Tuesday . Mnuchin said earlier Tuesday that the administration wants to get emergency funds in Americans' pockets "immediately."

Later Tuesday, Treasury Secretary Steven Mnuchin told GOP senators that unemployment could reach 20% if Congress doesn't enact the stimulus package, according to a person familiar with the situation.

The White House is seeking a stimulus package worth anywhere from $850 billion to more than $1 trillion as the Trump administration looks to battle the economic impact from the coronavirus pandemic, according to a source familiar with the matter.

Millionaires are unlikely to be among those who receive relief in the form of direct payments.

The White House will now have to negotiate a package with Congress. The measure will need to balance aiding individuals and workers in need, as well as industries it has already said it wants to support. The administration has made clear its view that the airline industry is essential. President Donald Trump and Mnuchin have also noted the cruise and hotel industries are facing particular challenges as travel has shut down.

"We're going big," Trump said at the presser. "We want to go big, go solid."

"We don't want airlines going out of business. We don't people losing their jobs," the president said.

Democrats, though, have made clear that any support to industries must come with significant aid to workers. There has already been dispute in Congress about paid time off in a second coronavirus relief bill, which has yet to pass the Senate.

"Any economic relief should be contingent on the benefits flowing to workers and their families, not CEOs and shareholders," Sen. Tom Udall, a New Mexico Democrat, told CNBC.

Sen. Elizabeth Warren on Tuesday outlined her own set of stipulations for any Big Business that receives federal bailout money. They include permanently giving up stock buy-backs and adding at least one seat to the board representing workers.

Senate Minority Leader Chuck Schumer's office said Monday that he will put forth his own plan with at least $750 billion in spending to combat the coronavirus pandemic. It would include forbearance on federal loans, a moratorium on evictions and foreclosures, assistance for small businesses and emergency child care.

Mnuchin said that the administration's plan will come into focus by "the end of the day" Tuesday.

The latest daily briefing came as stocks struggled to recover from one of the worst trading sessions ever a day earlier. Trump said in Monday's briefing that the U.S. may be able to get the new coronavirus outbreak under control by July or August at the earliest. Equities tanked as Trump delivered those remarks.

Major indexes rose during the coronavirus task force's briefing Tuesday, when Trump and his officials signaled that the administration was mobilizing a major economic response that would go into effect soon.

Markets have shed trillions of dollars amid the coronavirus spread, which has crippled major industries and forced governments around the world to take drastic steps to try to slow transmission of the disease. States and cities have taken sweeping measures to reduce social interaction, including limiting restaurants to delivery and takeout services. Other businesses have had to lay off and furlough employees.