By FRANK RICH — New York Times.

AFTER the dramatic three-month buildup, you’d think that Barack Obama’s speech announcing his policy for Afghanistan would be the most significant news story of the moment. History may take a different view. When we look back at this turning point in America’s longest war, we may discover that a relatively trivial White House incident, the gate-crashing by a couple of fame-seeking bozos, was the more telling omen of what was to come.

Obama’s speech, for all its thoughtfulness and sporadic eloquence, was a failure at its central mission. On its own terms, as both policy and rhetoric, it didn’t make the case for escalating our involvement in Afghanistan. It’s doubtful that the president’s words moved the needle of public opinion wildly in any direction for a country that has tuned out Afghanistan, Pakistan and Iraq alike while panicking about where the next job is coming from.

You can think the speech failed without questioning Obama’s motives. I don’t buy the criticism that he contrived a cynical political potpourri to pander to every side in the debate over the war. Nor was his decision to escalate mandated by his campaign stand positing Afghanistan as a just war in contrast to the folly of Iraq. Nor was he intimidated by received Beltway opinion, which, echoing Dick Cheney, accused him of dithering. (“The urgent necessity is to make a decision — whether or not it is right,” wrote the Dean of D.C. punditry, David Broder.)

Obama’s speech struck me as the sincere product of serious deliberations, an earnest attempt to apply his formidable intelligence to one of the most daunting Rubik’s Cubes of foreign policy America has ever known. But some circles of hell can’t be squared. What he’s ended up with is a too-clever-by-half pushmi-pullyu holding action that lacks both a credible exit strategy and the commitment of its two most essential partners, a legitimate Afghan government and the American people. Obama’s failure illuminated the limits of even his great powers of reason.

The state dinner crashers delineated those limits too. This was the second time in a month — after the infinitely more alarming bloodbath at Fort Hood — that a supposedly impregnable bastion of post-9/11 American security was easily breached. Yes, the crashers are laughable celebrity wannabes, but there was nothing funny about what they accomplished on Pennsylvania Avenue.

Their ruse wasn’t “reality” television — it was reality, period, with no quotation marks. It was a symbolic indication (and, luckily, only symbolic) of how unbridled irrationality harnessed to sheer will, whether ludicrous in the crashers’ case or homicidal in the instance of the Fort Hood gunman, can penetrate even our most secure fortifications. Both incidents stand as a haunting reproach to the elegant powers of logic with which Obama tried to sell his exquisitely calibrated plan to vanquish Al Qaeda and its mad brethren.

For all the overheated debate about what Obama meant in proposing July 2011 as a date to begin gradual troop withdrawals, the more significant short circuit in the speech’s internal logic lies elsewhere. The crucial passage came when Obama systematically tried to dismantle the Vietnam analogies that have stalked every American foreign adventure for four decades. “Most importantly,” the president said, “unlike Vietnam, the American people were viciously attacked from Afghanistan and remain a target for those same extremists who are plotting along its border.” This is correct as far as it goes, but it begs a number of questions.

“Along its border,” of course, means across the border — a k a Pakistan. Obama never satisfactorily argued why more troops in Afghanistan, where his own administration puts the number of Qaeda operatives at roughly 100, will help vanquish the far more substantial terrorist strongholds in Pakistan. But even if he had made that case and made it strongly, a larger issue remains: If the enemy in Afghanistan, whether Taliban or Qaeda, poses the same existential threat to America today that it did on 9/11, why is the president settling for half-measures?

It’s not just that Obama is fielding somewhat fewer troops than the maximum Gen. Stanley McChrystal requested. McChrystal himself didn’t ask for enough troops to fight a proper counterinsurgency in Afghanistan in the first place. Using the metrics outlined in the sacred text on the subject, Gen. David Petraeus’s field manual, we’d need a minimal force of 568,000 for Afghanistan’s population of 28.4 million. After the escalation, allied forces will reach barely a quarter of that number.

If the enemy in Afghanistan today threatens the American homeland as the Viet Cong never did, we should be all in, according to Obama’s logic. So why aren’t we? The answer is not merely that Afghans don’t want us as occupiers. It’s that such a mission would require a commensurate national sacrifice. One big difference between the war in Vietnam and the war in Afghanistan that the president conspicuously left unmentioned on Tuesday is the draft. Given that conscription is not about to be revived, we’d have to spend money, lots more money, to recruit the troops needed for the full effort Obama’s own argument calls for.

Which again leads us back to the ghosts of Vietnam. As L.B.J. learned the hard way, we can’t have both guns and the butter of big domestic projects, from health care to desperately needed jobs programs. We have to make choices. Obama paid lip service to that point, but the only sacrifice he cited in the entire speech was addressed to his audience at West Point, not the general public — the burden borne by the military and military families. While the president didn’t tell American civilians to revel in tax cuts and go shopping, as his predecessor did after 9/11, that may be a distinction without a difference. Obama’s promises to accomplish his ambitious plans for nation building at home while pursuing an expanded war sounded just as empty.

In this, he’s like most of the war’s supporters, regardless of party. On Fox News last Sunday, two senators, the Republican Jon Kyl and the Democrat Evan Bayh, found rare common ground in agreeing that an expanded Afghanistan effort should never require new taxes. It’s this bipartisan mantra that more war must be fought without more sacrifice — rather than Obama’s tentative withdrawal timeline — that most loudly signals to the world the shallowness of the American public’s support for any Afghanistan escalation. This helps explain why, as Fred Kaplan pointed out in Slate, the American share of allied troops in Afghanistan is rising (to 70 percent from under 50 percent at the time George Bush left office) despite Obama’s boast of an enthusiastic new coalition of the willing.

To his credit, Obama’s speech did eschew Bush-Cheneyism at its worst. He conceded some counterarguments to his policy: that the Afghanistan government is corrupt, mired in drugs and in “no imminent threat” of being overthrown. He framed his goals in modest and realistic terms, rather than trying to whip up the audience with fear-mongering, triumphalist sloganeering and jingoistic bravado. He talked of “success,” not “victory.”

But the president’s own method for rallying public support — a plea to “summon that unity” of 9/11 again — fell flat. There are several reasons why. First, 9/11 has been cheapened by the countless politicians who have exploited it, culminating with Rudy Giuliani. The sole achievement of America’s Former Mayor’s farcical presidential campaign was to render the evil of 9/11 banal. Second, 9/11 is eight years in the past. Looking at the youthful faces of the cadets in Obama’s audience on Tuesday, you realized that they were literally children on that horrific day, and that the connection between 9/11/01 and the newest iteration of the war they must fight in a new decade is something of an abstraction.

Finally, the notion that we are still fighting in Afghanistan because the 9/11 attacks originated there is based on the fallacy that our terrorist enemies are so stupid they have remained frozen in place since 2001. Most Americans know that they are no more static than we are. Obama acknowledged as much in citing such other Qaeda havens as Somalia (the site of a devastating insurgent suicide bombing on Thursday) and Yemen.

Americans want our country to be secure. Most want Obama to succeed. And so we hope that we won’t get bogged down in Afghanistan while our adversaries regroup elsewhere, that the casualties and costs can be contained, that the small, primitive Afghan Army (ravaged by opium, illiteracy, incompetence and a 25 percent attrition rate) will miraculously stand up so we can stand down. We want to believe that Obama’s marvelous powers of reason can check a ruthless enemy and reverse decades of tragic history in one of the world’s most treacherous backwaters.

That’s the bet Obama made. As long as our wars remain sacrifice-free, safely buried in the back pages behind Tiger Woods and reality television stunts, he’ll be able to pursue it. But I keep returning to the crashers at the gates, who have no respect for our president’s orderliness of mind and action. All it takes is a few of them at the wrong time and wrong place, whether in Afghanistan or Pakistan or America or sites unknown, and all bets will be off.