Presidential campaigns sometimes turn on big moments that help voters ponder the central question they have about every challenger: What would this person actually be like as president?

These aren’t the same as gaffes, which are slips of the tongue that may be politically damaging but say little about the candidates except that they misspoke.

I’m talking instead about critical moments of miscalculation -- often made in desperation -- that illuminate important truths about a politician.

In 1964, Barry Goldwater ardently defended extremism. In 1984, Walter Mondale said he would raise taxes. In 2008, John McCain suspended his campaign to work on the economic crisis and then offered no solutions for it. They all lost.

Now we have Mitt Romney, with astonishingly poor timing, trying to profit politically from tragic events in the Middle East. His remarks on Libya and Egypt at a news conference in Jacksonville, Florida, might or might not hurt his chances with pivotal independent voters in November. But we do know that he has managed to be simultaneously unpresidential, untruthful and unwise.

On the morning of Sept. 12, the world learned of the death of Ambassador J. Christopher Stevens, the first U.S. ambassador killed in the line of duty since 1979. Stevens died when terrorists attacked the U.S. consulate in Benghazi, Libya. At the same time, angry mobs breached the walls of the U.S. Embassy in Cairo.

Obvious Posture

The obvious and proper posture for a serious presidential candidate at that moment of shock and sadness would have been to show the country he could inhabit the role of mourner-in-chief, an important part of being president. Vows of justice are also welcome. Even if Romney couldn’t compete with President Barack Obama on this terrain, he needed to at least appear to be above partisan politics for a day or two.

Instead, Romney doubled down on a scorching statement issued the night before by his campaign that said: “It’s disgraceful that the Obama administration’s first response was not to condemn attacks on our diplomatic missions, but to sympathize with those who waged the attacks.”

In Jacksonville, Romney compounded his campaign’s slur with one of his own. “I also believe the administration was wrong to stand by a statement sympathizing with those who had breached our embassy in Egypt instead of condemning their actions,” he said.

Accusations that the Obama administration is somehow “sympathizing” with terrorists are false and, well, pathetic.

Here’s what the U.S. Embassy in Cairo, run by the Bush-era Ambassador Anne Patterson, wrote after mobs gathered outside in protest against a virulently anti-Muslim film associated with Koran-burning pastor Terry Jones:

The embassy “condemns the continuing efforts by misguided individuals to hurt the religious feelings of Muslims -- as we condemn efforts to offend believers of all religions,” it said. “We firmly reject the actions by those who abuse the universal right of free speech to hurt the religious beliefs of others.”

This is “disgraceful”? Really?

Read dispassionately, the statement is merely an effort by prudent diplomats to prevent a riot and bodily harm to Americans. It is almost identical to what the Bush administration said in 2006 after cartoons denigrating the Prophet Mohammad appeared in European newspapers: “We find them offensive, and we certainly understand why Muslims would find these images offensive.”

Was that also “akin to apology,” as Romney deemed the statement from the embassy in Cairo?

Republican Base

It’s hard to avoid the conclusion that the nominee is trying to pander to the Republican base, almost one-third of which still believes -- against all evidence -- that Obama is a Muslim.

In a fast-moving international crisis, facts can be confusing, which is why prudent leaders exercise caution. Not Romney, who was proud to shoot from the hip. “I don’t think we ever hesitate when we see something that is a violation of our principles,” he said at the news conference.

A little hesitation might have helped. Romney made it sound as if the statement by the U.S. Embassy in Cairo criticizing the anti-Muslim film was issued after the compound was under attack. It was issued before. A Twitter post reiterating the message, which the White House later said didn’t represent U.S. policy, was posted during the attack. But this, too, was nothing more than an effort to calm the “Arab street” and save lives.

To get a sense of how tone-deaf Romney’s news conference was, consider that former Alaska Governor Sarah Palin, Fox News political analyst Liz Cheney and William Kristol, the editor of the Weekly Standard, were just about the only Republicans to echo his message. House Speaker John Boehner, Senate Minority Leader Mitch McConnell, former Secretary of State Condoleezza Rice and McCain (though he assailed Obama on Libya the next day) all issued statements about Stevens’s death and the violence in Libya and Egypt. None included criticism of the Obama administration.

They understand that it’s not smart to use a tragic occasion to score political points even before the next of kin have been notified.

This fiasco may have originated with Romney, not his staff. In 2010, he wrote a book titled “No Apology” that charged Obama with issuing apologies for America in seven speeches at home and abroad in 2009. But Romney included not a single quote from any of those Obama speeches showing that the president actually apologized.

Is this what we want in a president? Imagine what would happen in the Arab world if a President Romney, pursuing his “No Apology” policy, expressed no regret when Korans were mistakenly destroyed by U.S. forces at a prison in Afghanistan, as they were earlier this year. The region would be ablaze for his entire time in office.

Americans recognize that judgment, prudence, instinct and a sense of what the moment demands are all job requirements for the presidency. Romney met none of them this week.

(Jonathan Alter is a Bloomberg View columnist and the author of “The Promise: President Obama, Year One.” The opinions expressed are his own.)

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To contact the writer of this article: Jonathan Alter at alterjonathan@gmail.com.

To contact the editor responsible for this article: Max Berley at mberley@bloomberg.net.