The proposal made on Tuesday as a part of financial aid packages that could add up to $1 trillion appeared to have the support of both Republicans and Democrats.
Trump and Treasury Secretary Steven Mnuchin did not reveal the specifics at a news briefing in Washington but in response to questions, they indicated that the amount could be in the range of $1,000.
Mnuchin said some people like millionaires would be excluded from the handouts.
Hundreds of thousands of Americans are expected to lose their jobs at least temporarily because of the closing of businesses under government orders and due to fall off in customers.
Trump wants the cheques to reach the public "within two weeks", Mnuchin said.
He said the administration preferred cash payments, rather than indirect payments through tax cuts or deferments, so the money could be sent out within two weeks.
He said that the details were being worked out on the exact amount and how to get the money to the people "now."
A group of Democratic Senators have proposed sending $4,500 to all Americans, indicating broad support for a payment plan.
Mnuchin later met Republican Senators to push the payments plan and other parts of an economic stimulus package totalling $850 million.
Of this, $250 million would be earmarked for loans to small businesses.
Earlier, the House of Representatives had passed a $100 billion economic package, which the Senate is scheduled to take up this week.
The stock markets that had registered a historic fall of about 13 per cent on Monday recovered somewhat on Tuesday regaining about five per cent.
The financial urgency and scale of the proposed intervention exceeds government bailout package of $700 billion for banks after the 2008 economic crisis.
Trump sounded upbeat about getting the rescue plan through Congress, saying "there's great spirit" among lawmakers.
Trump said he wants to "go big to blunt the economic pain caused by the coronavirus. "I don't want to do incremental stuff and keep coming back to it," Trump said.
(Arul Louis can be contacted firstname.lastname@example.org and followed on Twitter @arulouis. Nikhila Natarajan can be reached at email@example.com and followed on Twitter @byNikNat)