A good picture, as everybody knows, is worth a thousand words. The one that appeared on the front page of The New York Times last Thursday could also be worth a hundred congressional votes.

Extracted from a video smuggled out of Syria, the frame showed gunmen about to kill seven prostrate and terrified army soldiers, their backs bared and beaten, their hands tied behind their backs, as a rebel commander ranted a bloody oath of revenge. Such are the Islamist extremists that the US would in effect be supporting, the picture declared with a starkness no words could match, if the Obama administration went ahead with its threatened military strikes against the Assad regime. Who knows: could this be what tips the balance in the upcoming congressional debates, the image that undermines not just Barack Obama's foreign policy during the rest of his term, but America's very role in the existing world order?

An exaggeration? Not really. Last week's fraught G20 summit in Russia – at which he spent as much time telephoning wavering Senators and Congressmen back home as he did interacting with his fellow leaders near St Petersburg – was but a prelude. Beyond doubt, these next few days will be the most crucial of the Obama presidency. Tomorrow the Senate starts its debate on a resolution authorising military strikes to punish the Assad regime for its presumed use of chemical weapons against its fellow citizens. On Tuesday evening, in a televised address, Obama will seek to persuade the nation why that should happen, by which time the House of Representatives may have taken up its own resolution on the subject.

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Two votes, on which he has, to all intents, bet his presidency and his legacy. Yet it didn't have to be like this. When Obama announced last weekend that he had decided to go ahead with bombing and missile strikes against Syrian government installations, yet would seek the approval of Congress beforehand, he was turning political practice on its head.

Formal declarations of war are the exception in US history; the most recent were against Japan, Germany and Italy when America entered the Second World War. In reality a commander-in-chief does not even need congressional permission to use force. What tends to happen – as in the fateful 1964 Gulf of Tonkin resolution that greased the slope to the Vietnam war, and most recently in the October 2002 resolution allowing George W Bush to invade Iraq – is broad authorisation some while before the event.

A couple of times (over the 1999 air strikes against Serbia, and an extension of US involvement in the 2011 campaign against Muammar Gadaffi in Libya) Congress has actually voted against military operations. But Bill Clinton on the first occasion, and Obama on the second, went ahead regardless. This time, however, Obama is seeking narrow and specific approval of a brief and largely symbolic campaign, one meant not to overthrow the Assad regime, merely to "fire a shot across its bows", that will see not a single American boot on the ground in Syria.

Or rather, that's what's meant to happen. But a country that's fed up with wars – particularly wars of choice in a treacherous, ungrateful Middle East where no direct US interests are at stake – just isn't buying that argument. As in Britain, the average American hasn't forgotten the intelligence fiasco that produced the last Iraq war. And what if Assad or his allies retaliate? Might not America be dragged into a wider conflict that turns the threat of regional conflagration into reality?

Faced with such public scepticism, Obama himself admits it will be a tough sell, one that even his rhetorical gifts cannot guarantee. On Capitol Hill the arithmetic is no less daunting. In the Senate, traditionally the more moderate and considered chamber, and where Obama's Democrats have control, there's a 50-50 chance, maybe slightly better, of a yes vote. But the House of Representatives is another matter.

You start with a Republican majority reflexively opposed to everything this President does. But the opposition cuts across party lines, as liberal, anti-war Democrats make common cause with the libertarians and America-first Tea Partiers on the far Republican right. As of Friday evening, according to The Washington Post, 224 of the 433 current House members were opposed to US military intervention and barely two dozen in favour, despite the long-range arm-twisting by the White House. If anything, moreover, hostility is growing. Some even speculate that a resolution will not even be put to the vote, to spare not so much Obama as the institution of the presidency, and American credibility in world affairs.

Some would argue the President could follow his example of two years ago, and simply ignore the opinion of Congress. But having gone out of his way to seek that opinion, that course would seem inconceivable, not to mention politically calamitous. A House spurned will be even less likely to compromise, as new showdowns loom over the budget, a possible government shutdown and renewal of the federal debt ceiling. Even impeachment proceedings are possible. They would be a mere stunt of course, but a distracting and demeaning one for Obama.

And last but not least, the Pentagon itself is opposed to war. So much was evident from the testimony (or lack of it) to the Senate last week by the country's top uniformed soldier, General Martin Dempsey, chairman of the Joint Chiefs. And consider this summary of the views of serving commanders from Robert Scales, a retired army general well plugged in to US military thinking. The brass, he wrote in the Post, was "embarrassed to be associated with the amateurism of the Obama administration's attempts to craft a plan that makes strategic sense", and a path to war "that violates every principle of war". They were, he went on, "outraged" at the prospect of an act of war merely "to make up for a slip of the tongue about 'red lines'". Withering stuff. Unlike Congress, the military ultimately does what it's told, however reluctantly. Whatever happens, however, a presidency is on the line this week.