V, it turns out, is not for vendetta. It’s for Vietnam. In the long, bitter debate before the Iraq war it was always war opponents who brought the V-word up. Many of us who never lived through that nightmare shrugged it off. It was another baby-boomer neurosis, we thought. America had fought and won wars since then, notably the first Gulf war. America had liberated Afghan Muslims and protected Bosnian Muslims, without the “quagmire” so many warned about. It became a point of pride for war supporters to deny outright any Vietnam comparison as preposterous.

So it made news when last week the president himself confirmed that the analogy had some bite. He was asked about a recent analogy from Thomas Friedman, a columnist, who had compared the current moment in Iraq to the 1968 Tet offensive when Vietcong guerrillas in the south and North Vietnamese troops launched a joint attack and prompted a collapse in morale in the American heartland. “He could be right,” George W Bush said. “There’s certainly a stepped-up level of violence and we’re heading into an election.”

The president didn’t mean, mind you, that the United States was losing. He was reiterating what has long been a common view among neoconservatives: that the Tet offensive was a military failure for the Vietcong, which was crushed, but a profound PR success for the communist North. The lesson neoconservatives drew was that America will not falter, as it did in Vietnam.

“The full context was that the comparison was about the propaganda waged in the Tet offensive,” the White House explained later. “The president was reiterating something he’s said before — that the enemy is trying to shake our will.”

Consider it shaken. The polls suggest plummeting support for the war and deep discontent with the president and Congress. And the reason, it must be conceded, is similar to the reason in the Vietnam war. The US is now in a classic counter-insurgency war, just as it was in Vietnam. Its superior firepower is of no use in such a situation, just as carpet-bombing Vietnam and Cambodia couldn’t turn the Vietnamese population into allies of a foreign intervention.

Worse, the military has even less knowledge and intimacy with the culture and history of Iraq than it did in Vietnam. It has no South Vietnamese to deploy as spies and informants. Without that knowledge, and without support from a functioning government on the ground, the military risks becoming paralysed by a maze of tribal, sectarian and religious forces that it can neither understand nor master.

On a practical basis this means that American soldiers can clear a town of insurgents but when the Americans leave the insurgents return and, in the absence of a powerful central government, the inhabitants have no option but to co-operate with the enemy. The government’s own forces are either incompetent or infiltrated by the very militias that are fomenting the sectarian conflict in the first place. And so the war grinds on, with little chance of victory.

A political solution, the only secure way to achieve peace in Iraq, has slipped across the horizon, as Sunni Arabs, Shi’ite Arabs and Sunni Kurds recoil into the protection of the clan, the tribe and the ethnic or religious family. After each round of violence a cycle of revenge follows.

And so the Iraqi civilian casualties mount to something like 3,500 a month. We can argue about numbers but it remains indisputable that the number of deaths in Iraq is now surpassing the murderous levels of the previous dictatorship. The Americans look on, fighting hard in some places, resigned to stalemate elsewhere.

If you look up such a situation in a dictionary, you’ll stumble across the V-word eventually. But the analogy still doesn’t hold. In terms of American casualties there is no comparison. The toll in Vietnam was 20 times that of Iraq — and there was a draft (conscription to you Brits), so the cost of warfare was brought home powerfully across America. Today’s volunteer military both minimises such casualties and protects most Americans from the war’s terrible toll.

In other respects the analogy is flawed because the situation in Iraq is worse than Vietnam. When South Vietnam fell, the consequences were largely restricted to the region. They were awful — as the toll of communism culled hundreds of thousands in Cambodia and Vietnam. But they ended at the ocean.

In Iraq the consequences of American withdrawal could be a full-scale civil war, widespread ethnic cleansing, and the involvement of Iran, Syria, Saudi Arabia, Jordan and even Egypt in a potentially catastrophic Sunni-Shi’ite conflagration. Add to that the possibility of Turkey intervening in Kurdistan and you could have the region with a chokehold on the world’s energy supplies turning into a corpse-ridden, Balkan desert.

Worse, withdrawal could allow for a failed state — or even region, like Anbar province — to become a training camp for jihadists to wage war on the West from a safe haven in the Middle East. Unlike Vietnam, this could bring the war home to America’s own cities. Or to London. Or Paris or Madrid or Tel Aviv.

If victory is impossible and defeat unimaginable, what can America do? One answer is the one given by Dick Cheney, the vice-president, and Donald Rumsfeld, the defence secretary: denial. Last week Cheney said the government of Nouri al-Maliki, the prime minister of Iraq, was doing “remarkably well”. Sadly for Cheney the number of Americans willing to believe this is now much lower than the number who believe the Earth was made in seven days 6,000 years ago.

And so the smart money in Washington, especially if the Democrats retake part or all of the Congress on November 7, is on some sort of deal with the neighbouring regimes to stabilise and police Iraq.

The Bush family consigliere, James Baker, has been asked to come up with a plan. It may take talking directly to Iran and Syria, something that will represent a real volte-face for the White House. It may mean reaching out to Jordan, the Saudis, and even the Russians for direct or indirect negotiation with the various factions in Iraq — or with Iran and Syria.

Just as a chastened America will have to cede managing the North Korean crisis to China, so it will have to pass on some of the burden for containing Iraq to its neighbours. It’s a high-risk strategy — but so are all the alternatives.

More important: it will be an acknowledgment that the project as it has been understood for the past three years is now over. But we will have to wait until after the elections to know exactly what lies ahead.

Times Recommends

• We have kit and leadership. Let’s go
• Behind the scenes at the biggest deal
• Conferences — what a waste of money