Congressional leaders and White House officials began work Monday on a massive new coronavirus relief bill that could contain major economic stimulus for corporations and consumers, aiming to move the legislation through the Senate as soon as this week as President Trump warned a recession could be coming.

Senate Majority Leader Mitch McConnell (R-Ky.) said Congress’ third coronavirus relief bill should include further steps to assist individual Americans and families; actions to secure the economy and small businesses; and additional steps to shore up the health care system and support medical professionals who are expected to be overwhelmed in coming weeks. “The Senate is committed to meeting these uncertain times with bold and bipartisan solutions,” McConnell said.

The legislation is likely to carry a price tag in the hundreds of billions of dollars, reminiscent of the bailouts and stimulus packages Congress was forced to enact in the 2008 financial crisis.

Work on the new piece of legislation follows enactment earlier this month of an $8.3 billion package focused on the public health care system, and House passage last week of a bill aimed at safety net programs including sick leave, unemployment insurance and food stamps. Monday evening, Treasury Secretary Steven Mnuchin -- who negotiated the House bill with Speaker Nancy Pelosi (D-Calif.) -- and other top administration officials met with GOP senators at the Capitol to discuss next steps and push for quick action.

“We have a real focus on urgent action. And I’m hopeful that there could be swift consideration of consensus ideas as quickly as possible,” White House legislative affairs director Eric Ueland said after the meeting, emphasizing the overall size of the proposal would likely be enormous.

“The president has instructed his team to look very expansively at what we need to do and not be impeded by the potential price tag of what’s necessary here,” Ueland said.

Sen. Marco Rubio (R-Fla.) said that the treasury secretary, who is planning to attend the weekly Senate GOP lunch Tuesday, is expected to present an overall dollar figure for the new proposal. Rubio said that the Senate would needed to act swiftly to help the economy but also because the health crisis is deteriorating to a level where members of Congress won’t be able to travel back and forth to their states each week.

"I think the assumption’s going to be that we’re going to do something, it should be big. Because we can’t assume that we’re just going to keep coming back,” Rubio told reporters after the meeting.

“We are basically telling people not to go out, not to spend money at these stores. …. It’s an unprecedented challenge,” Rubio said.

Industries including airlines, cruise lines and casinos have been seeking Congress’ help as everyday life in America screeches to a halt under the growing coronavirus threat. Stocks took another beating Monday as the Dow Jones industrial average closed down nearly 3,000 points. The disruptions caused by the pandemic spread to all corners of society as schools closed nationwide and the federal government recommended against gatherings with more than 10 people. At a meeting with his coronavirus task force, Trump said in response to a question that the economy “may be” headed into a recession.

Senate Finance Committee Chairman Charles E. Grassley (R-Iowa) said the forthcoming package under development by his committee and others would “help families and businesses with immediate cash-flow needs to get through the immediate crisis and provide a broader economic stimulus for Americans and industries across the country.”

Senate Democrats also have an ambitious wish-list. Minority Leader Charles E. Schumer (D-N.Y.) proposed a $750 billion package to address everything from hospital capacity and loan forbearance to treatment affordability and remote learning.

“We will need big, bold, urgent federal action to deal with this crisis,” said Schumer, whose proposals did not include industry bailouts. “The kinds of targeted measures we are putting together will mainline money into the economy and directly into the hands of families that need it most.”

GOP senators discussed Schumer’s proposed $750 billion pricetag -- and concluded their package could end up being even costlier, Rubio said.

On a House Democratic conference call, House committee chairs discussed ideas including: cash payments to individuals; infrastructure investments; expanded Medicaid spending; anti-price-gouging measures; airline industry support; and assistance to local transit agencies and Amtrak, according to a person on the call who spoke on the condition of anonymity to discuss it. The list is expected to evolve although Democratic leaders hope to have a firmer package of proposals toward the end of the week.

First, though, the Senate must act on legislation passed by the House last week that devotes tens of billions of dollars to new paid sick leave benefits, unemployment insurance, free coronavirus testing, and food safety programs. The legislation -- which passed just before 1 a.m. Saturday after a flurry of last-minute negotiations -- required technical changes that threatened to hold up Senate action. Those legislative fixes were hammered out Monday and passed by the House Monday evening.

A few Republican senators voiced objections or concerns about various provisions in the House bill, such as the structure of new sick leave mandates on small businesses. But administration officials sounded optimistic about getting the House bill through the Senate with minimal drama. After playing little role in developing the most recent bill, however, McConnell and Senate Republicans seemed eager to shape the next package, especially since the House is out of session this week and everyone wants to move swiftly.

The third package is likely to include pouring additional federal funding into improving public health infrastructure to deal with the outbreak, according to congressional aides. Funding for local transit authorities and cleaning supplies to disinfect city subways and buses have also come up as likely critical needs, according to one person with knowledge of internal discussions.

The measure is also likely to include the biggest actions to date to assuage broader concerns of an economic slowdown. The payroll tax cut called for by the president has gotten a lukewarm reception by lawmakers in both parties, but it is unclear exactly what other broad-based stimulus measures could receive bipartisan support. Democrats and a handful of Republicans have backed disbursing direct cash payments to tens of millions of poor and middle class Americans to help them weather the downturn. Among these is Sen. Mitt Romney (R-Utah) who released a proposal Monday stating: “Every American adult should immediately receive $1,000 to help ensure families and workers can meet their short-term obligations and increase spending in the economy.”

Romney said after the meeting with administration officials Monday evening that he believed "there’s interest” in his plan.

Republican aides are also exploring whether the next coronavirus package makes sense as a vehicle for an infrastructure package, according to a lobbyist with knowledge of internal discussions.

Other measures likely to be included could take aim at strengthening the federal safety net even more. Democratic lawmakers are eyeing much more aggressive expansion of unemployment insurance as firms are expected to rapidly shed jobs. Democratic lawmakers are also likely to push for a much larger expansion of Medicaid than the one approved in the initial House package. Officials fear rising unemployment could lead to a dramatic surge in the number of Medicaid beneficiaries, which could financially hamstring states just as state tax revenue also take a hit from declining business activity.

Targeted financial help for specific industries is also widely expected in the next package, although some lawmakers are skittish about advancing bailouts for large firms at a time of widespread economic uncertainty. The Trump administration has said it will work with Congress on financial help for the airline, cruise, and hospitality industry. Senior administration officials are considering zero-interest loans and tax deferrals, among other measures.

--Mike DeBonis contributed to this report.