U.S. President Donald Trump on Thursday said federal workers could be fired and projects cut if a government shutdown continues, even as he suggested Americans might get rebate checks from new tariff revenues.

"There could be firings, and that's their fault," Trump said of Democrats in Congress, when asked in an interview with OAN television network about a recent memo from the Office of Management and Budget that raised prospects of firings.

"We could cut projects that they wanted, favourite projects, and they'd be permanently cut," he said, adding, "I am allowed to cut things that should have never been approved in the first place, and I will probably do that."

The federal government partially shut down on Wednesday after Congress failed to reach a funding deal, with only essential services continuing.

Trump said revenues from new tariffs were just starting to kick in, but could eventually reach $1 trillion a year. He said some of the funds would help pay down the government's debt, which he said could reach $38 trillion.

Trump's tariff estimate far exceeds that of Treasury Secretary Scott Bessent, who last month said customs duty revenues from Trump's tariffs could top $500 billion a year.

U.S. Treasury data shows the federal government has $37.64 trillion in federal debt.

The Republican president said his administration was looking at using tariff revenues to issue rebate checks for Americans.

"We also might make a distribution to the people, almost like a dividend to the people of America," Trump told OAN.

"We've thinking maybe $1,000 to $2,000. It'd be great."