Forget a debate. President Donald Trump and former Vice President Joseph R. Biden Jr. want to throw down with their fists.

Back in 1804, Vice President Aaron Burr and political rival Alexander Hamilton chose to settle their deep differences in perhaps the most American way, with guns. But Biden and Trump want to face off in an even more old-school way, by throwing hands.

Biden on Wednesday — for the second time — said he would like to “beat the hell out of” Trump. The next morning, Trump accepted the challenge, tweeting that the longtime senator and 2020 Democratic presidential frontrunner would “would go down fast and hard, crying all the way.”

The exchange offered a potential 2020 general election preview, suggesting the two men with very different backgrounds, demeanors, views of the presidency and political beliefs would not hold back in their rhetoric toward one another.

Watch: Emerging Omnibus Plan Lacking Some Big-Ticket Trump Asks

Nebraska Republican Sen. Ben Sasse was not impressed by the Trump-Biden war of words. 

Sasse fired off a tweet describing the capital city as locked in “total dysfunction.” He made clear his distaste for a $1.3 trillion spending measure both chambers could pass as soon as Thursday, and then offered this about the 45th president and the former VP spoiling for a fight: “Meanwhile both of our crazy uncles are fistfighting in the backyard. Happy Thanksgiving, America.”

Total dysfunction. DC is about to add 1.3 TRILLION $ to your debt like it’s no big deal – and meanwhile both of our crazy uncles are fistfighting in the backyard. Happy Thanksgiving, America. https://t.co/qFfqdtJKkE

— Senator Ben Sasse (@SenSasse) March 22, 2018

The 75-year-old Biden issued his second challenge Wednesday during remarks at the University of Miami about going mano a mano with the 71-year-old Trump, who once got physical with World Wrestling Entertainment’s Vince McMahon and WWE superstar “Stone Cold” Steve Austin at WrestleMania 23. Trump took down McMahon at one point, but later was on the receiving end of Austin’s finishing maneuver, the “Stone Cold Stunner.”

“They asked me would I like to debate this gentleman, and I said no. I said, ‘If we were in high school, I’d take him behind the gym and beat the hell out of him,’” the former VP said.

That prompted Trump to lash back on Thursday morning.

He dubbed his potential fistfight foe “Crazy Joe Biden” and mocked him for “trying to act like a tough guy.” In the president’s view, Biden is “weak, both mentally and physically.”

[With Omnibus, Trump Learning You Can’t Always Get What You Want]

Then the 45th president of the United States appeared to accept Biden’s apparent challenge, yet another twist in an unpredictable and chaotic — though he and his aides detest that description — presidency.

“He doesn’t know me, but he would go down fast and hard, crying all the way,” Trump wrote.

[Watch: Emerging Omnibus Plan Lacking Some Big-Ticket Trump Asks]

He then lectured Biden about threats — even though he had just threatened the former vice president. “Don’t threaten people Joe!” he wrote.

Crazy Joe Biden is trying to act like a tough guy. Actually, he is weak, both mentally and physically, and yet he threatens me, for the second time, with physical assault. He doesn’t know me, but he would go down fast and hard, crying all the way. Don’t threaten people Joe!

— Donald J. Trump (@realDonaldTrump) March 22, 2018

The back-and-forth conjured memories of 1804, when Burr shot Hamilton dead. Burr was never charged with a crime in that illegal duel.

The Secret Service has not yet issued a statement about the sitting chief executive throwing hands, even though his military doctor contends Trump is in fine physical condition for a man in his early 70s.