On Tuesday, top White House economic adviser Larry Kudlow said the US$ 2 trillion stimulus bill would work in tandem with US$ 4 trillion in bolstered lending power from the Federal Reserve.
Investors had welcomed news that agreement on the package was near. Wall Street bounced back on Tuesday from three-year lows on word the negotiators were close to a deal.
Trump, who is campaigning for re-election on Nov. 3, has said he wants Americans to return to work more quickly than many medical experts had advised. On Tuesday, he set a target of the April 12 Easter holiday, which would ease a public health clampdown intended to slow spread of the virus.
To become law, the stimulus deal must pass the Senate, where Republicans hold a slim majority, and the House of Representatives, which is led by Democrats, and then be signed by the Republican president.
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Mnuchin told reporters after the agreement was announced that Trump "absolutely" would sign it if it passed Congress.
The package "is going to be very important to help American workers, American businesses and people across America," he added.
Mnuchin urged House Speaker Nancy Pelosi to quickly schedule a vote on the measure once it clears the Senate. Aides to Pelosi, the top Democrat in Congress, did not immediately respond to a request for comment when the deal was announced well after midnight.