Barack Obama puts a brave face on it. The Afghan war is winnable, he insists. "We are going to break the Taliban's momentum," he told US troops at Bagram this month. He repeated the mantra today. But American commentators and analysts, across the political spectrum, are wondering aloud: will it happen the other way around? Will the war break Obama's presidency?

Obama is not yet the Rose Garden prisoner of a failed policy – the fate that befell a Democrat predecessor, Jimmy Carter, whose administration was taken hostage by Iran's revolutionary mullahs. But he's uncomfortably close, for all the determined White House talk.

Obama the presidential candidate talked up the war, spoke of fighting the good fight in Afghanistan in contrast to Iraq, wrote Peter Feaver in Foreign Policy. But Obama the president struggles to communicate his aims, much as he struggled on healthcare. Feaver said:

"The administration's strategy appears to be to drive the public narrative underground."

In other words, Obama would rather not talk about it unless he cannot avoid it.

This reluctance is political and intellectual. Veteran foreign policy analyst Leslie Gelb, writing in the Daily Beast, said Obama can no longer persuasively answer the basic question: why are 100,000 American troops in Afghanistan, at an annual cost of $113bn?

"Afghanistan is no longer a vital interest of the United States but continuing the war there tears at our own nation's very vitals," Gelb said, arguing that international terrorism now has many bases, including Stockholm and London, and is no longer centred in the Hindu Kush (if it ever was). He added:

"With America drowning under a $1.5tn deficit for next year and an almost $15tn overall debt, we are verging on banana republic-hood... Of course I feel for the Afghans; but I feel far, far more for Americans."

Obama's electoral vulnerability, waging a war he can't explain and can't afford, is explored further by the conservative columnist George Will. With US casualties at record highs and public support falling, Will speculated about a repeat not of Carter's misfortunes but of Lyndon Johnson's:

"Taliban leaders surely know that North Vietnam won the Vietnam war not in Vietnam but in America. And they surely known the role played by North Vietnam's 1968 Tet offensive. Although US forces thoroughly defeated the enemy, the American public, seeing only chaos and the prospect of many more years of it, turned decisively against the war."

On this analysis, the all-powerful General David Petraeus can "surge" the reinforcements Obama sent him as long as he likes. Increased violence has the opposite effect to that intended. It strengthens the general's most potent foes – who stand behind him, not in front of him.

These "foes" include a majority of the public, the CIA (which believes that Pakistani support for the jihadis is fatally undermining the whole counter-insurgency project), many Democrats in Congress, White House containment advocates such as vice-president Joe Biden, and maybe even Obama himself.

To a degree, he was trapped by his own stump rhetoric. But insider accounts suggest Obama knows in his heart he was bounced into an escalating conflict by a bunch of Iraq-tainted military top brass keen to prove they can win a war. He sacked generals McKiernan and McChrystal. But he can't sack 'em all.

Obama, of course, is adamant that a phased troop drawdown will begin next July. But the real deadline has been pushed back and back. As they say in Kabul: "2014 is the new 2011". And even that may not stick, especially if sections of the Afghan security forces continue their impersonation of Dad's Army.

All the same, next summer may still prove to be showdown time for Obama's war – for both his presidency and his hopes of a second term. "Obama's most ardent political supporters are the most fervent opponents of his war policies," said Feaver. If limited July, 2011 withdrawals "start a rapid rush to the exit", as the American left hopes, the Republicans whose votes have sustained Obama will desert him. If Obama adheres to Petraeus's slower, "conditions-based" withdrawal through 2014 and beyond, Obama may lose his political base. "Any remaining left-leaning props undergirding public support will likely collapse altogether," Feaver predicted.

Will makes the same point a different way. Whether Obama is re-elected in 2012 "depends partly on whether the party's left, which provides a disproportionate portion of the party's energy, is energised," he said, adding:

"Whatever one thinks of the current strategy, Obama is prosecuting it with a vigour that indicates a refusal to allow political calculations to condition national security. This presidential virtue could imperil his presidency."

Analyst Tony Cordesman, quoted in Politico, said Obama had six months to show results – or face the electoral consequences. "Few in America or outside it will be willing to hear another explanation of why the new strategy has not yet been validated in the field."

The writing is on the wall for Obama. The latest opinion poll, published yesterday by the Washington Post/ABC News, is chilling for the White House. A record 60% of Americans now believe the war is not worth fighting; only 45% approve Obama's handling of the conflict.

A more telling statistic perhaps is that 54% of Americans support the July 2011 start date for beginning troop withdrawals, while 27% say they should start sooner. According to a separate poll this month, a majority of Afghans also believes the US and Nato should leave by mid-2011 or earlier.

This clamour cannot be ignored indefinitely. If Obama allows his generals to drag their feet, and the casualties keep mounting, he risks a political meltdown and the destruction of his presidency.