Aside from the question of legality, some have also asked whether Trump’s offer would be feasible financially in the context of increasing US debt, partially as a result of the war in Iran.
There are nearly 270 million American adults, meaning a $5,000 payout would cost the US government some $1.3 trillion.
Trump gave no details on how such cheques would be funded.
Congress authorises spending in the US, but the president did not say whether he planned to ask for legislative approval for any payments.
And legal experts said it was unlikely he could approve such a vast sum via a presidential executive order.
Erica York, a senior economist at the Washington DC-based Tax Foundation, told the BBC she would be “extremely surprised” if Congress approved any proposal.
“This would be one of the worst ways to use $1.3 trillion,” she said.
“We’re on a very unsustainable track, with deficits only projected to grow and grow,” York added.