The controversy was yet another reminder, a few days ahead of America's birthday, that Trump is a leader like no other in the nation's 241-year history, who plans to stay true to himself and is willing to flout norms of decorum.
The longer such antics go on, more and more people will question whether the leader of the free world is not just damaging his own presidency, but demeaning the office itself and potentially diminishing it for whoever comes after him.
"It's unworthy of the office of President of the United States," Maine Sen. Susan Collins told CNN's Anderson Cooper. "And I am concerned about how we look in the eyes of the world as well as our own citizens."
Republican Rep. Adam Kinzinger of Illinois told CNN's "New Day" Friday "that's a tweet that's not even becoming of a city councilman."
Thursday's tweets focused attention on Trump's coarse brand of political discourse, and his ironclad principle that anyone who criticizes him, as Brzezinski did on her show on Thursday, can expect a gut punch in return.
His tweet outraged political leaders in Washington and renewed debate about the President's history of disparaging remarks about women. It left allies fuming about yet another day when his political agenda was drowned out by Trump-induced tumult.
But on a deeper level, the shocking tweet, which claimed that the "Morning Joe" host had been "bleeding badly from a facelift," raised questions about whether his behavior was appropriate from a head of state, about his respect for his office itself, and whether this presidency could irrevocably erode the standards of dignity that have grown around it since George Washington swore the first oath of office in New York City in 1789.
The New York Daily News revealed its Friday cover -- a bald eagle, head hanging down as if in shame, with "humiliation" in capital letters.
Brzezinski and her co-host and fiancee Joe Scarborough hit back at the President on their show Friday morning, prompting a new blast from Trump on Twitter as their feud escalated.
"We're OK. The country is not," Scarborough said on "Morning Joe," and accused the President of harboring a "disturbing obsession with Mika."
Brzezinski said Trump's behavior was "frightening and really sad for our country."
The President was tuned in, and tweeted that he "Watched low rated @Morning_Joe for first time in long time," and branded the show "FAKE NEWS."
Trump's tweet was set to generate another day of discussion in Washington about whether his conduct was becoming of a President.
But, for a sense of proportion, it might also be said that his tweets, while often misrepresenting facts and dealing in personal attacks, pale in comparison to the actions of some of his predecessors. Also casting the presidency in a poor light were President Bill Clinton's Oval Office encounters with an intern and President Richard Nixon's cover-up that led to his resignation over the Watergate scandal.
And respect for the presidency, like many other institutions, was declining long before Trump tried his hand at politics. In 1991, 93% of Americans polled by Gallup had some level of respect
for the presidency. By June 2016, that number was down at 63%.
Yet Trump's demeanor obviously falls short of the elevated standards established by the likes of Washington, Abraham Lincoln or Ronald Reagan, and appears to risk fraying that faith in his office still further.
Unlike some of those leaders, it is not clear that Trump regards the presidency as a public trust to be preserved and passed onto successive generations. He often seems more concerned with his own image than the reputation of the presidency itself, as his fixation with the size of his election victory and inauguration crowds has revealed.
He's exactly the same
Trump does not exist in a vacuum. He is an expression of a polarized political age that lacks civility, shaped by reality television and instant emotional kick of social media that has shattered political and societal norms. In many ways, Trump seems to be exactly the same personality who lived out his life in the New York tabloids and swapped smutty stories with radio host Howard Stern.
So far at least, he doesn't seem to be changed by the responsibilities heaped on his shoulders.
But while his unchained style helped him win the presidency, it may be undermining his chances of significant achievements now that he is in office.
That's because the presidency is more than a job. The pageantry, from the Oval Office, to the "beast" limousine, to Air Force One as it jets into a foreign land, conjures up a mystique and a statement of power -- that Trump appears not yet to have harnessed to its full potential.
His White House's war with the media, the chaos that pervades the administration, and the fact the President dispels his own elevated aura by inviting the world into his mind every day on his Twitter feed also seem at risk of diminishing the unique power and prestige of his office.
Many Presidents were flawed men who made questionable moral choices. But most at least tried to keep their anger and most unguarded inner thoughts private, a safety valve that Trump seems to lack.
Trump's tweet was far from his only outrageous comment as a candidate or a President. But it appeared to set off a pent-up explosion of anger towards Trump over weeks of patience-fraying political tribulations.
Republican Sen. Lindsey Graham of South Carolina tweeted: "Mr. President, your tweet was beneath the office and represents what is wrong with American politics, not the greatness of America."
Alaska Sen. Lisa Murkowski tweeted: "Stop it! The Presidential platform should be used for more than bringing people down."
House Speaker Paul Ryan, who normally swerves away from Trump tweets, said this one was not "appropriate" and didn't help efforts to change the political tone. Pennsylvania Republican Sen. Pat Toomey told CNN's Jake Tapper it was "maddening."
In some ways, the outpouring of criticism toward Trump was surprising precisely because his attack on Brzezinski was not all that surprising.
After all, he has a long record of incendiary comments toward his perceived opponents in the media, and directed at women particularly.
During his campaign, he insulted John McCain's war record, made vulgar comments about then Fox News anchor Megyn Kelly and berated the grieving Muslim parents of a fallen war hero. As President, he claimed he was being wiretapped by the previous administration without evidence and seemed to suggest he may have tapes of conversations with FBI chief James Comey.
This time it seemed different, perhaps because the bullying tweet aimed at Brzezinski was another tweet targeted from the White House -- the people's house -- by a man who is the President of all Americans.
That may explain why few came to Trump's defense, save for his loyal deputy press secretary Sarah Huckabee Sanders, in an abrasive encounter with the White House press corps.
"The President has been attacked mercilessly on personal accounts by members on that program, and I think he's been very clear that when he gets attacked, he's going to hit back," Huckabee Sanders said.
"They do this day after day after day, and then the President responds and defends himself and everybody is appalled and blown away," she added.
But Trump's skin does seem particularly thin. Presidents have long been mercilessly attacked but have often chosen to respond in a manner in keeping with the dignity of an office that Washington called an "arduous trust" in his farewell address.
The last two Presidents, for example, have often fumed privately. After the Iraq War degenerated into a bloody insurgency, George W. Bush was relentlessly attacked over his intellect and leadership skills. But he rarely snapped in public.
President Barack Obama, the first African-American commander in chief, endured a character assassination over claims he was not even born in the United States -- conducted by Trump himself -- and only rarely displayed his public disgust for his accuser.
Trump's supporters, by this time, are well used to his eruptions on Twitter and elsewhere, and may shrug their shoulders at his assault on a mainstream media figure.
In fact, Huckabee said, Trump's bombast was the reason he is in the White House.
"The American people elected somebody who's tough, who's smart, and who's a fighter, and that's Donald Trump. And I don't think that it's a surprise to anybody that he fights fire with fire," she said.
History suggests it will take more than explosive tweets to tarnish the Oval Office.
"I am not sure that any damage to the office will be permanent because I cannot see another President like Trump being replicated," said Lori Cox Han, an author and professor who teaches courses on the presidency at Chapman University, California.
"I think of the office of the presidency as being incredibly resilient -- it survived Bill Clinton's impeachment, Richard Nixon's resignation ... survived the Civil War," Han said. "It and our Constitution will survive Trump -- no matter what side of the aisle you happen to be on."