If a president is judged by a growing slice of the population to have abdicated his office's traditional imperative to provide steady, moral and unifying authority, where does the nation turn next?

The fallout of Donald Trump's stunning news conference Tuesday has focused largely on the equivalence he appeared to draw between white supremacists and protestors opposing their marches in Charlottesville.

But now a debate is also stirring over whether Trump's remarks have irrevocably severed any chance of this president ever commanding the support, or even the respect, of a majority of the country's population.

Presidents, in their dual role as the figureheads of their administrations -- and heads of state -- are often called upon to summon the country's resolve, principles and unity at times of crisis or political discord.

Even his supporters would concede Trump has never made much attempt to reach out beyond his own base, proving more skillful at exploiting societal divisions for political gain than bringing people together. And there is no sign he plans to start now.

Two sources told CNN's Jeff Zeleny the President was defiant and "without regret" over his combustible performance Tuesday, likening the outraged media response to some of the volcanic twists of his campaign.

Photos: Violence erupts at a white nationalist rally in Charlottesville, Virginia People fly into the air as a vehicle drives into a group of people demonstrating against a white nationalist rally after police cleared Emancipation Park in Charlottesville, Virginia, on Saturday, August 12. Hide Caption 1 of 17 Photos: Violence erupts at a white nationalist rally in Charlottesville, Virginia The vehicle moments before it struck the crowd. Hide Caption 2 of 17 Photos: Violence erupts at a white nationalist rally in Charlottesville, Virginia A woman receives first aid after a speeding car slammed into this silver convertible as it navigated through a crowd of counterprotesters. Hide Caption 3 of 17 Photos: Violence erupts at a white nationalist rally in Charlottesville, Virginia A man embraces an injured woman after a car rammed into the crowd. Hide Caption 4 of 17 Photos: Violence erupts at a white nationalist rally in Charlottesville, Virginia Right-wing rally members clash with counterprotesters in Emancipation Park, where white nationalist groups gathered for a rally. Hide Caption 5 of 17 Photos: Violence erupts at a white nationalist rally in Charlottesville, Virginia A counterprotester strikes a white nationalist with a baton during clashes at Emancipation Park, where white nationalists are protesting the removal of the Confederate Gen. Robert E. Lee monument. Hide Caption 6 of 17 Photos: Violence erupts at a white nationalist rally in Charlottesville, Virginia A counterprotester throws a newspaper box at a right-wing rally member at the entrance to Emancipation Park. Hide Caption 7 of 17 Photos: Violence erupts at a white nationalist rally in Charlottesville, Virginia A counterprotester uses a lighted spray can against a white nationalist at the entrance to Emancipation Park. Hide Caption 8 of 17 Photos: Violence erupts at a white nationalist rally in Charlottesville, Virginia Counterprotesters try to burn a Confederate battle flag taken from white nationalist protesters. Hide Caption 9 of 17 Photos: Violence erupts at a white nationalist rally in Charlottesville, Virginia White nationalists, neo-Nazis and members of the "alt-right" clash with counterprotesters. Hide Caption 10 of 17 Photos: Violence erupts at a white nationalist rally in Charlottesville, Virginia A white nationalist is seen with a cut below his eye suffered during clashes with counterprotesters at Emancipation Park . Hide Caption 11 of 17 Photos: Violence erupts at a white nationalist rally in Charlottesville, Virginia White nationalists, neo-Nazis and members of the alt-right movement exchange volleys of pepper spray with counterprotesters as they enter Emancipation Park. Hide Caption 12 of 17 Photos: Violence erupts at a white nationalist rally in Charlottesville, Virginia A woman is treated for exposure to pepper spray during clashes between white nationalists and counterprotesters at Emancipation Park. Hide Caption 13 of 17 Photos: Violence erupts at a white nationalist rally in Charlottesville, Virginia White nationalists use shields as they guard the entrance to Emancipation Park. Hide Caption 14 of 17 Photos: Violence erupts at a white nationalist rally in Charlottesville, Virginia Counterprotesters line the route taken by white nationalists and neo-Nazis during the "Unite the Right" rally. After clashes with anti-fascist protesters and police, the rally was declared an unlawful gathering and people were forced out of Emancipation Park, formerly called Lee Park and home to a controversial statue of Confederate Gen. Robert E. Lee. Hide Caption 15 of 17 Photos: Violence erupts at a white nationalist rally in Charlottesville, Virginia White nationalist Richard Spencer and his supporters clash with Virginia State Police in Emancipation Park. Hide Caption 16 of 17 Photos: Violence erupts at a white nationalist rally in Charlottesville, Virginia Riot police form a line of defense in front of the statue of Confederate Gen. Robert E. Lee in Emancipation Park, recently renamed from Lee Park. Hide Caption 17 of 17

"The public is learning (even more so) how dishonest the Fake News is. They totally misrepresent what I say about hate, bigotry etc. Shame!" he tweeted Thursday morning.

But barreling ahead and recommitting to the rhetoric that outraged people across the political spectrum could cost the President any goodwill he still has left among people who don't support him. That in turn would compromise his capacity to unite the nation during a crisis or when the next political volcano erupts.

An NPR/PBS NewsHour/Marist poll released Wednesday revealed the depths of Trump's problems. His approval rating was plumbing new depths at 35%, suggesting that only his loyal political base is sticking with the President.

Some 52% of those polled said the President's reaction to Charlottesville was not strong enough -- only 27% said it was.

With poll numbers that grim -- more typical of a seventh year in office for a president rather than a seventh month -- it is questionable whether Trump can lead the country anywhere.

A search for political leaders

If Trump cannot provide leadership, then the question becomes: Who can?

Damaged presidencies often result in Congress taking on a more prominent role, shouldering more of the burden of running the country.

But this Congress is even more unpopular than Trump.

A growing list of top Republicans, including Sen. John McCain and Sen. Lindsey Graham, appear to fear the toxic impact of Trump's remarks on their party and have criticized the President, taking advantage of their prominence and independent power bases to speak out.

Others, like Sens. Marco Rubio and Ted Cruz and Ohio Gov. John Kasich, are in the top tier of potential future presidential candidates who have criticized Trump and are playing a game of risk and possible reward.

But taking advantage of the August recess, House Speaker Paul Ryan and Senate Majority Leader Mitch McConnell stayed out of sight. Both decried the content of Trump's comments but avoided a personal rebuke.

"We can have no tolerance for an ideology of racial hatred. There are no good neo-Nazis, and those who espouse their views are not supporters of American ideals and freedoms," McConnell said in a statement.

"We all have a responsibility to stand against hate and violence, wherever it raises its evil head."

Ryan offered similar sentiments in a tweet Tuesday.

"We must be clear. White supremacy is repulsive. This bigotry is counter to all this country stands for," he said. "There can be no moral ambiguity."

We must be clear. White supremacy is repulsive. This bigotry is counter to all this country stands for. There can be no moral ambiguity. — Paul Ryan (@SpeakerRyan) August 15, 2017

While few people would disagree with those fine sentiments, neither leader came across as a profile in courage, since condemning neo-Nazis ought to be the easiest thing a big-time politician would ever do.

While the Ryan/McConnell position makes political sense since most Republicans still back Trump, it's hardly courageous.

There's always the Democrats.

And they have spoken as one in outrage at Trump's remarks. But the party is still working through the trauma of Hillary Clinton's presidential election defeat last year and is yet to offer America a compelling political personality or message to break through the Washington cacophony.

Democrats are an afterthought in Washington anyway, since the GOP runs the House and the Senate. And this early in the political cycle, it's not clear any unaffiliated voters are pining for Democratic leadership.

In fact, the only Democrat whose example has broken through in Washington is a leader from the past, not the future -- Barack Obama.

The former president's message quoting Nelson Mandela has just become the most liked tweet in history.

Two other former commanders in chief, George H.W. Bush and George W. Bush, also leveraged the power of their legacies to decry racial discrimination in a clear swipe at Trump in an unusual breach of the normal protocol of the ex-presidents club. Neither mentioned Trump by name in their statement.

Emerging leaders beyond politics

Outside the political world, some prominent figures have taken a stand.

Kenneth Frazier, the CEO of Merck & Co, resigned from Trump's manufacturing council to take a stand against the President's remarks about Charlottesville on Saturday.

He triggered a mass exodus of CEOs that forced Trump to close down two advisory councils -- an embarrassing blow to his claims to be a business tycoon president who could use his corporate pals to reinvigorate the economy.

And while Frazier braved Trump's Twitter wrath and was the first to exit, you would not have to be a cynic to conclude that the subsequent rush of CEOs to desert Trump had as much or more to do with concern for their blue chip brands than a sudden desire to honor civil rights.

In the arts and media, Trump critics have pounced. Late-night hosts dropped comedy routines for social commentary about Trump's racial rhetoric.

Editorial boards across the nation excoriated the President. The Chicago Sun-Times branded him "America's Bigot-in-Chief."

But since many conservatives revile the media, the chances that journalists and entertainers can bring the country together are slim.

There is one institution that still appears to have bipartisan clout: the military.

Five joint service chiefs, apparently conscious of the racially integrated nature of their services, have now condemned white supremacists.

Chief of Naval Operations Adm. John Richardson tweeted as far back as Saturday: "Events in Charlottesville unacceptable and musn't be tolerated @USNavy for ever stands against intolerance & hatred."

In another post, on Wednesday, Chief of Staff of the Army Gen. Mark Milley posted: "The Army doesn't tolerate racism, extremism, or hatred in our ranks. It's against our Values and everything we've stood for since 1775."

None of the posts, from sources who take pains to be nonpartisan, mentioned Trump specifically. But they were extraordinary all the same.