"You'd have to pick him up off the floor," McAuliffe said.
"You mean you'd deck him?"Matthews sputtered after bursting out laughing.
"You want to get in my space, I've always said, Chris, you punch me, I'm going to punch you back twice as hard," McAuliffe replied with a straight face. "And it wouldn't be hard to do it but you know, this guy thinks he can intimidate everybody. It's disgraceful, it's embarrassing but I tell you when we take him on, back in his face, with the facts, don't take anything from him and hit him back as hard as you possibly can. But if he ever came over and leaned on me and got in my space, that would be the last time Donald Trump ever did that. I promise you that."
McAuliffe, a longtime Democratic insider and fundraiser before he was elected to office in 2013, is an ebullient politician known for hyperbole, traits that irk some in Virginia's staid political culture. But veiled threats of violence, even if in jest, are new ground for him.
He's criticized Trump plenty before, but has been mindful of going too overboard given how reliant Virginia's economy is on the federal government. Some of his harshest criticism of the president came after Trump suggested "both sides" were to blame after white nationalists and counterprotestors violently clashed in Charlottesville over the summer.
On "Hardball", McAuliffe called Trump "an embarassment to our country" after The Washington Post and other outlets reported that he objected to bringing in immigrants from "shithole" countries during a meeting.
"He's an embarrassment to our country," McAuliffe said. "I mean, he comes off looking like a lunatic saying things like this, disparaging individuals. You know, we need to bring this country together. We need to work together. He just doesn't have an ability to be able to do it. He is hurting everyone's ability to grow jobs and do what we need to do to be successful."
McAuliffe went on to say that voters "have had it with Trump" and that Republicans who stand by him "are going to pay a huge price at the polls", predicting that Democrats will win back the House and Senate in November.
But the line suggesting he'd literally beat Trump got more notice.
"Omg President McAuliffe sounds pretty good!! 2020," one person tweeted.
Susan Swecker, chairwoman of the Democratic Party of Virginia, tweeted "Gov McAuliffe standing up to bullies, no matter who they are."
Conservative media also took note: Drudge Report prominently featured a headline blaring "McAuliffe says he'd slug Trump" high on its page.
An anti-Trump wave helped Democrats resoundingly win in state elections in November, sweeping all three statewide offices and nearly wiping out the Republican majority in the House of Delegates.
On Saturday, McAuliffe will be succeeded by his far more low-key lieutenant governor Ralph Northam, who called Trump a "narcissistic maniac" during Virginia's primary but later said he would work with him.
Asked how Northam would respond to Trump hovering over him, his spokeswoman texted, "Probably laugh."