It's likely House leaders will try to pass the bill by unanimous consent.
Trump had voiced hope Tuesday that the country could begin to reopen by Easter but his top infectious disease advisor, Anthony Fauci, said the timetable would need to remain "very flexible".
Senate leaders noted the historic nature of the challenge posed by the coronavirus, which the Democratic Senate Minority Leader Chuck Schumer called "a unusual and evil disease".
State and local authorities would receive up to $150 billion in grants to fight the virus, care for their residents and provide basic services.
The bill sets aside $250 billion for direct payments to individuals and families, $350 billion in small business loans, $250 billion in unemployment insurance benefits and $500 billion in loans for distressed companies.
In a major relief to hospitals, the bill provides $130 billion. Couples making up to $150,000 would receive $2,400, with an additional $500 per child.
The drive by leaders to speed the bill through the Senate was slowed as four conservative Republican senators from states whose economies are dominated by low-wage jobs demanded changes, saying the legislation as written might give workers like store clerks incentives to stay on unemployment instead of return to their jobs since they may earn more money if they're laid off than if they're working. In addition, it establishes worker protections attached to federal loans for businesses, and it prohibits airlines from using the funds for CEO bonuses. The Treasury Department would have to disclose the terms of loans or other aid to companies and a new Treasury inspector general would oversee the lending program. Businesses owned by members of Congress, heads of executive departments and Vice President Mike Pence also would be blocked.
One of the provisions tucked into the massive coronavirus relief bill approved by the Senate late Wednesday night restricts certain businesses that accept government loans in their dealings with labor unions.
Wall Street stocks closed mixed Wednesday as the markets awaited a vote on the rescue package, the third of its kind in the past month, but by far the largest.
The agreement is an expansion of a Republican legislative proposal issued last week, dubbed the CARES Act - the Coronavirus Aid, Relief, and Economic Security Act - to provide relief to virtually every rung of the US economic ladder.
Schumer also said that hundreds of billions would be spent on Democratic priorities, including the expansion of unemployment benefits, money for hospitals as well as more funding for cities and transportation.
Democrats also rejected the $3 billion sought by the Trump administration to buy oil to fill the Strategic Petroleum Reserve.
Senate Majority Whip John Thune, South Dakota Republican, was one of the latest to miss the votes; he flew home Wednesday because he wasn't feeling well.
"I think the American people will assess the progress that's been made for workers as a result of taking a little bit of extra time for hospitals and for state and local governments who are going to benefit mightily because of the work that we've done", Bennet said Monday on the Senate floor.
It dwarfs the bailouts of 2008, when a worldwide financial crisis sent the United States economy into a tailspin.
Together with Fed intervention, the proposed legislation amounted to a $6 trillion stimulus, according to White House economic adviser Larry Kudlow, or about 30 per cent of annual GDP.
Cuomo said health officials anticipate about 120,000 coronavirus patients coming into New York's hospitals, which have a capacity of 50,000 beds.
An initial $8 billion plan passed by Congress March 5 is funding emergency health care needs stemming from the coronavirus, and a second plan enacted last week will provide many Americans with paid sick leave, food assistance and free coronavirus testing. It also will send tens of billions in fresh aid to states.