(CNN) The coronavirus' relentless spread is exposing Donald Trump to a question no president wants to hear: Is he up to the job?

For supporters and opponents alike, questions about Trump's basic competence as a manager of the federal government have taken a back seat during his presidency to the fierce controversies over his personal behavior, his language (particularly on issues relating to race and culture) and his policy agenda.

But the federal government's unsteady response to the outbreak threatens Trump with the same public verdict that ultimately undermined predecessors such as Jimmy Carter during the Iranian hostage crisis and George W. Bush after Hurricane Katrina: a belief that he is simply overmatched by the practical demands of the presidency -- though he gave himself a perfect 10 rating on Monday for his handling of the crisis.

"It's what happened with Jimmy Carter in the hostage thing: [The public concluded] he's incompetent, he doesn't know what he was doing," says Matthew Dowd, a former senior strategist for Bush. "Once that was happening, it didn't matter what else he did. The same was true of George W. Bush, once the Katrina thing crystallized it. Once those things happened neither one of them ever recovered."

Trump hasn't yet reached that tipping point: Polls so far show that public attitudes about his handling of the outbreak almost completely track the long-standing divisions around his overall job performance. But Democrats believe the cascading risk created by the virus is highlighting aspects of Trump's personality and management style that Americans were more willing to tolerate before the nation faced such an acute and disruptive challenge.

"There have been long-standing character flaws that people believe Trump has: Namely, he's chaotic, and he's selfish and egotistical," says Jesse Ferguson, a Democratic strategist. "Those character flaws have not always come with consequences until now. ... If you weren't worried about his character flaws before, you may become worried now that you see his character flaws come with a price."

Ideology vs. competence

The unprecedented scale and reach of the coronavirus challenge will test the assumption among many political experts that in our highly polarized political era , ideological and cultural affinity is eclipsing results in office as the principal determinant of a president's support.

Since the 1990s, political strategists and political scientists alike have concluded that more and more Americans are permanently locked into each party's coalition, with fewer swing voters available for either side to woo.

In effect, that judgment means that the share of voters who support a president based on his ideology and cultural identity is growing, while the portion that bases its decisions on the president's performance is shrinking. In terms of the public's approval of a president, results such as the state of the economy or his handling of a crisis "are probably less important now than they used to be, because with increasing polarization everything comes down to partisanship and policy agreement," says Alan Abramowitz, a political scientist at Emory University.

In a recent national survey by the nonpartisan Pew Research Center , fully 87% of Republicans -- and almost two-thirds of all whites without college degrees -- said that Trump fights for what they believe in.

Most observers believe that through this approach Trump has forged a bond with his political base that will prove impervious to almost any questions about his response to the coronavirus outbreak or the economic slowdown that appears certain to accompany it.

"His hard-core supporters who like his approach, his style and are with him on immigration and the wall, all these things, the racial resentment ... it's hard for them to perceive him as incompetent because they are so invested in him," says Abramowitz. "There's also an issue of perception here. It doesn't necessarily affect his hardcore supporters; they are watching Fox News, they are getting their information from places that are still pretending that he's doing a great job of handling this, or initially it was no big deal, it's fake."

But most experts in both parties agree the political base that passionately embraces Trump's rhetoric and agenda is probably closer to 40% than 50% of the electorate. To win reelection, Dowd notes, Trump needs another "8 to 10 points" of ambivalent voters who may be conflicted about his behavior or policy priorities but have been satisfied with the results of his presidency, particularly on the economy. Those are the voters, Dowd argues, who "do put a premium on competence."

Doubts are hard to recover from

Questions about competence have played a kind of all-or-nothing role in the assessments of modern presidents. Few presidents have confronted serious questions from the public about whether they could handle the job. Presidential candidates have struggled to make competence a central campaign issue, probably because most Americans assume anyone who advances as far as a major party's nomination is qualified for the Oval Office.

In 1988, then-Democratic presidential nominee Michael Dukakis sought to place competence at the heart of his race against then-Vice President George H.W. Bush. ''This election isn't about ideology," Dukakis famously declared in his acceptance speech at the Democratic National Convention. "It's about competence."

Over the next few months, Bush's campaign emphatically proved Dukakis incorrect: The vice president wiped out the Democrats' early lead in the polls with a bruisingly ideological campaign that portrayed the Democrat as a "Massachusetts liberal" who was soft on crime and weak on national defense.

Bush's victory solidified a view in both parties that promising competence alone wasn't enough to win the White House. A generation later, former New York City Mayor Michael Bloomberg learned the same lesson, when he failed to win a single state in the Democratic primaries this year after a massive advertising blitz that touted his managerial skills. ("The presidency is a management job," Bloomberg tweeted at one point during his campaign.)

But while a perception of managerial competence doesn't guarantee success in presidential campaigns, the opposite impression may still be fatal. As Dowd notes, the relatively few presidents who have faced doubts about their baseline capacity to handle the job -- Carter heading into 1980, George W. Bush during his second term, Herbert Hoover during the Depression -- found it almost impossible to recover from them.

Don Kettl, a professor of public policy at the University of Texas at Austin who has written extensively on government management, said the testing delay will rank among the most sweeping and consequential federal failures ever.

"In terms of failure, it's hard to remember something on this scale," he said. "People go back to Katrina as one example. And that was a monumental failure, but in one community. The problem is this has been multiplied across the country at a scale that puts everyone at jeopardy. Government simply has dropped the ball."

A question of timing

That verdict, though widely shared among public health experts, hasn't yet transcended the nation's political divide. Recent national Quinnipiac and NBC/Wall Street Journal surveys have found that slightly more Americans disapprove than approve of Trump's handling of the outbreak, but that in each case those views almost exactly matched the preexisting perceptions of his performance. In both surveys, about 85% of the people who approved of Trump's overall job performance also gave him positive marks for handling the coronavirus, while a comparable number of those who disapproved of his overall performance gave him a negative grade, according to detailed results provided by the pollsters. The share of Americans who approved of his response to the coronavirus in these surveys was little changed from the 43% who told Gallup last year that they believed he could manage the federal government effectively.

Even perceptions of the underlying threat are following the familiar partisan tracks. With many conservative media outlets, led by Fox News , echoing Trump in downplaying the risk, the NBC/WSJ poll found that self-identified Republicans were much less likely than Democrats to consider the virus a danger or to report that they were changing their activities in response to it.

"I just can't recall anything where the basic facts of anything so fundamental have to go through a political filter and the perception [of what's happening] depends on which side of the fence you are on," said Kettl.

These poll results show just how difficult it is for any new information to cross the long-standing political chasm between red and blue, which has widened further under Trump. Yet it may be premature to conclude that questions about his handling of the virus, and the likely economic fallout, will not ultimately affect his standing.

Ferguson, an adviser to Navigator Research, a Democratic organization that studies public opinion and messaging, says the crisis is forcing attention to many aspects of Trump's behavior that voters remain most uncomfortable about. The group's polling , he says, has found that most Americans believe that Trump's response has been incompetent, untrustworthy and more concerned about protecting his political interests than public health.

"Voters had preexisting notions about Trump on his character, his competence and his health care agenda, and this crisis has confirmed their worst fears about all three," Ferguson argues. "More of the country has doubts about his ability to do the job than at any point since he was sworn in."

One possible measure of those concerns: Those polled in the latest Quinnipiac survey, by a resounding 56% to 40% , said they had more faith in former Vice President Joe Biden, the likely Democratic nominee, than in Trump to handle a crisis. Almost three-fifths of independents picked Biden.

Abramowitz says the timing of the outbreak also could magnify Trump's political risk. Most academic models that study the impact of the economy on presidential campaigns, he notes, consider economic growth in the second quarter of the election year, the period beginning in April, as the decisive factor.

"The second quarter, from our modeling, seems to be the one that matters the most -- that's the one that seems to shape attitudes going into the election," Abramowitz says. And several economic forecasters , including at Goldman Sachs , are now projecting a sharp contraction during that second quarter.

Ultimately, even in a highly polarized era, Trump may prove hostage to events. Perceptions about his handling of the crisis today may not look the same if more Americans see tangible impacts in their own lives, especially beyond the big Democratic-leaning metropolitan areas that already have responded most aggressively. Public health officials warn that the outbreak may not peak for weeks. At best that means disruption of ordinary life will continue well into the spring; at worst, it could mean chaotic scenes of hospitals overrun as the caseload and death roll rise.

The political arguments over Trump's response, Kettl says, "in a sense, are not going to matter in a week or two, because the facts will bear out which side of the fence turns out to be right. If it turns out what the President has said is counter to what the virus decides to do, that could very well be his Katrina moment but multiplied 1,000 times over. The (virus) itself will decide which side is right on this one."