As Smith's team has noted in arguing against Trump, the former president's lawyers during his second Senate impeachment trial said in very clear terms that they believed a president could in fact be criminally prosecuted by the Department of Justice -- the opposite of what his legal team is currently arguing.

"If my colleagues on this side of the chamber actually think that President Trump committed a criminal offense -- and let's understand, a high crime is a felony and a misdemeanor is a misdemeanor; the words haven't changed that much over time -- after he is out of office, you go and arrest him," one of his attorneys said in opening statements during his impeachment trial in 2021, shortly after Jan. 6.

"We have a judicial process in this country, we have an investigative process in this country, to which no former officeholder is immune,” Trump's attorney said then.

But now, facing federal charges related to Jan. 6, Trump's lawyers argue a president can only be prosecuted if he is impeached, convicted by the Senate and removed from office.

The Senate in his second impeachment trial acquitted, though a majority of lawmakers voted to convict him.

-ABC News' Katherine Faulders

Trump appeared confident while addressing the presidential immunity hearing during remarks Thursday morning in Manhattan.

"We have a big case today -- this judge wouldn't allow me to go, but we have a big case today at the Supreme Court on presidential immunity, a president has to have immunity," Trump said at a construction site where he met with union members, workers and supporters. "If you don't have immunity, you just have a ceremonial president," he insisted.

When asked about the justices, three of whom he named to the high court, Trump said, "They're very talented people, they're very smart, they know what they're doing."

Trump stopped by the midtown Manhattan site, where the new JPMorgan headquarters is under construction, before heading to the courthouse for his hush money trial. He denies all wrongdoing.

-ABC News' Lalee Ibssa, Soo Rin Kim and Mike Pappano

Trump, seeking to quash the federal election subversion case brought against him by Smith last year, is claiming he has “absolute” immunity from the criminal prosecution for anything related to his presidency.

Two lower courts have rejected that argument.

First, District Judge Tanya Chutkan (who is overseeing the trial) determined that someone once serving as president “does not confer a lifelong 'get-out-of-jail-free' pass.”

Then, a three-judge panel on the U.S. Court of Appeals for the District Court of Columbia unanimously struck down Trump's claims. They warned his view, if accepted, would “collapse” the country's political system.

Trump then appealed to the U.S. Supreme Court. His trial is on hold while this matter plays out in the courts.

Justice Clarence Thomas opened questioning by getting to the heart of the case: where is the "source" of presidential immunity and how would the court come to decide what acts fall under that scope.

First, he asked Trump's attorney to be "more precise as to the source" of supposed presidential immunity.

John Sauer responded that it comes from the executive vesting clause of the Constitution.

Thomas then pressed how exactly the court would "determine what an official act is," to which Sauer said acts fall within the “outer perimeter” of a president's official duties.