Some time in the next two weeks, Mr Obama is likely to bring months of agonised deliberation to a close when he decides how many more troops to send to Afghanistan. The number, which could be as high as the 40,000 recommended by Stanley McChrystal, the general in charge, will be analysed minutely for what it can achieve on the ground in Afghanistan.

But as Mr Cheney’s contrasting observations illustrate, the more influential war is being fought politically on the ground in America. Somehow, the compulsions of US politics have brought the candidate who electrified America by promising to pull out of Iraq to a position where many of his most ardent backers fear he may be about to get America into another Vietnam.

The decision, much like the one by Lyndon Johnson to step up involvement in Indochina, could prove to be the most important Mr Obama takes in office. It presents America’s most liberal president in a generation with a classic dilemma between guns and butter that is only likely to deepen, whatever choice he makes.

“What began as an almost reflex debating stance on the campaign trail – that George W. Bush had started the wrong war in Iraq and that Hillary Clinton had voted for it – has brought us to this moment,” says Daniel Markey at the Council on Foreign Relations. “Only now is the president really analysing the implications of escalation in Afghanistan. And they are potentially paralysing.”

Some believe the analogies with Vietnam are overdone: The US lost almost 60,000 lives in south-east Asia against the 797 it has so far lost in Afghanistan. But the parallels are also inescapable. Much like LBJ, Mr Obama is being dragged reluctantly into a war that threatens to interfere with an ambitious domestic programme of liberal reform. Much like LBJ, Mr Obama is surrounded by the “best and the brightest”, many of whom are urging the president to take the advice of the military, which appears to be nearly unanimous.

And much like Vietnam, the war in Afghanistan is viewed in Washington as a proxy for a larger ideological battle – the former against worldwide communism, today against Islamist terrorism. In both cases, the president is asked to take a gamble on the response of complex faraway societies that are only fleetingly understood. In both cases, there is a recurring suspicion that the smartest minds at the Pentagon are looking for a nail to fit their hammer.

“The real nail is in Pakistan,” says Larry Wilkerson, a retired army colonel who was chief of staff to Colin Powell, the former secretary of state. “But there is only a limited amount we can do to influence what happens there.”

This week, Mrs Clinton’s touchdown in Pakistan coincided with one of the worst terrorist attacks it has experienced, leaving 100 dead in the back alleys of Peshawar. The secretary of state’s arrival followed months of terrorist escalation in a country where the military is only now perceived to be putting significant – if questionable – weight behind operations targeting Taliban sanctuaries in the tribal areas. Mrs Clinton, who leaves Pakistan on Saturday, has received a cool reception in spite of the fact that Congress recently approved another $7.5bn (£4.6bn, €5.1bn) of civilian aid for the troubled country.

According to a recent poll, 59 per cent of Pakistanis view America as their greatest threat, against just 18 per cent for India and 11 per cent for al-Qaeda. America’s aid package was greeted with suspicion and derision across Pakistan. “I have never had so much difficulty in trying to give away $7.5bn,” said John Kerry, chairman of the US foreign relations committee, on a trip to Pakistan last week.

Senator Kerry’s own experience in the region underscores Mr Obama’s dilemma. The former presidential candidate played what many saw as a decisive role in persuading Hamid Karzai, the Afghan president, to go ahead with a second round of voting after an August presidential election in which monitors had declared almost one-third of his votes to be fraudulent. Mr Obama is expected to make his troops announcement only after the run-off, which takes place a week from Saturday.

Many in the White House were hoping that Mr Kerry’s recent diplomatic feat would stiffen his resolve to support Mr Obama’s forthcoming troop surge and thus help reconcile the liberal wing of the Democratic party to this “war of necessity” – as opposed to the “war of choice” Mr Cheney and Mr Bush commenced in Iraq.

But their hopes were dashed – and the deep ambivalence of many of Mr Obama’s non-military advisers was underlined – when Mr Kerry gave a confusing speech back in Washington this week. The Vietnam war veteran said that Gen McChrystal’s proposed counter-insurgency strategy went “too far, too fast”. But the senator also said a US pull-out from Afghanistan could be dangerously destabilising for the broader region.

“Kerry had an opportunity to put his shoulder to the wheel,” says one outside adviser to Mr Obama. “Instead he chose to sit on the fence.” Sitting on the fence is a luxury Mr Obama cannot afford. But many in Washington, both Democrats and Republicans, are predicting the president will split the difference by choosing to send in 20,000-30,000 more troops rather than the 40,000 or more Gen McChrystal has requested.

Following the worst month of the war so far – with 45 Americans killed in October – Mr Obama paid a pre-dawn visit to Dover air force base in Delaware on Thursday to salute the caskets of the returning American dead. Then, on Friday, he held the seventh Oval Office discussion with senior military staff and advisers on Afghanistan – and not necessarily the last before he takes his decision.

Nobody doubts Mr Obama’s intellectual ability to parse the constant advice he is soliciting. Nor do people doubt his understanding of the great weight that falls on the shoulders of America’s commander-in-chief – as his visit to Dover illustrated. But almost everybody – including, reportedly, the Taliban – doubts whether Mr Obama’s heart is in this war.

“My guess is that he’ll announce something north of 20,000 troops and hope that is enough,” says Peter Bergen, an expert on al-Qaeda, who is urging a full-scale counter-insurgency. “Then he will work out what can be done with that number and when results can be announced. For example, it would take 2,000 US troops to secure the road between Kabul and Kandahar. That could be done by next summer.”

By then the other ground war – the one on US political terrain – will also be hotting up with midterm congressional elections taking place next November. In the 1966 midterms, much of the steam was taken out of LBJ’s presidency when his party suffered setbacks at the polls because of the escalating war in Vietnam. Next week, electoral analysts predict, the Republicans will retake the governorship of Virginia, a state that Mr Obama won handily last November. Many of the liberals who populate northern Virginia around Washington are expected to sit on their hands – a sense of disillusion already sinking in.

The question facing Mr Obama is whether he can get results from Afghanistan in time to trumpet success back home. That was also LBJ’s preoccupation: his obsession with a domestic political timetable made for deteriorating relations with the generals.

“My concern is that we get, say, a 20,000 troop increase but with instructions to Gen McChrystal to achieve results on an unrealistic timetable,” says Bobby Wilkes, a retired air force general, who was a senior Pentagon official in the Bush administration. “If you don’t put in enough troops now, you may have to put in more later.”

To put it another way, splitting the difference and announcing 20,000-plus new troops might look like the least risky choice. But it would satisfy neither liberal nor conservative critics of Mr Obama back home. And it may do little to convince the Taliban that America is in this fight for keeps.

“The one thing the White House is determined to avoid is to repeat the mistakes of Vietnam,” says Mr Markey. “But in trying to avoid the mistakes of Vietnam, it could simply be making a whole new set of mistakes.”