Governments and generals, the complaint runs, are forever refighting their last war. In the case of the United States and Syria today, that rule holds true – to which one can only say, thank heavens.

Europe edges closer to arming Syria's disorganised and fractious rebels. Russia sends more arms to the odious Assad regime which, reports suggest, appears to be regaining the upper hand in the fighting. But the biggest question is the US. What will Washington, which alone has the military capability to decide the conflict quickly, do? Thankfully the answer, so far at least, has been – nothing.

Syria is the problem from hell. Over 70,000 have been killed, atrocities have been committed by both sides, millions of refugees are placing huge strains on neighbouring countries. Directly or indirectly, everyone is involved: Iran, Lebanon, Iraq, Israel, Turkey, Russia. Daily, the risk grows of a regional sectarian war between Shias and Sunnis. And no one is in control.

President Obama, however, surveys the scene and sees no good option. US intervention, he concludes, would only make matters worse. Having repeatedly called for regime change, there is no way Washington could claim to be an honest broker, imposing a no-fly zone and safe havens, or even putting US boots on the ground, purely for humanitarian reasons. Obama wants Assad out. But he reasons that the best hope, however tiny, of an end to the carnage is the conference the US and Russia hope to convene next month.

But there's another dynamic at work too, the fixation with "the last war". The phenomenon can be traced back to Vietnam. America's humbling there cast a long shadow into the future, right up to the next major US war, to evict Saddam Hussein from Kuwait. If ever a war was "right" it was that one – to reverse a tyrant's seizure of a neighbouring country, in defiance of all international law. To further legitimise the use of force, President Bush Snr assembled a massive international coalition, including several Arab countries, backed by the Soviet Union as well. Yet Congress barely passed a resolution authorising the war. Such was the baleful influence of Vietnam.

A dozen years later, the reverse was true. The "coalition of the willing" that Bush junior assembled for his 2003 invasion of Iraq was tiny compared with his father's. The war's legitimacy was contested by France, Germany, Russia and others, Britain was the only ally of significance. But the first Gulf war had been a breeze, and the Senate overwhelmingly approved. The ayes included several Democrats, among them John Kerry, now Secretary of State, who had voted no in 1991.

This time of course, the expected "cakewalk" didn't materialise. The invading Americans were not greeted with garlands of flowers. There followed an eight-year occupation that cost 150,000 Iraqi lives, 4,500 US lives and $1trn (£660bn).

Obama isn't squeamish about using force (witness his troop surge in Afghanistan and his expanded use of drones). But as he declared at the time, the 2003 invasion was a "dumb" war. A repeat in Syria, in circumstances even more complicated, would be as dumb, if not dumber.

Yes, there are similarities, not least a dictator who, like Saddam, may have used chemical weapons against his own people. And there's a vocal domestic lobby for intervention, led by John McCain who last weekend went to Syria to meet some rebel leaders, and reborn Cold War warriors who claim the Russians are running rings around the US, and Obama is projecting US weakness – the ultimate sin – by refusing to step in.

But a majority of Americans agree with Obama. Like him, they saw one long and messy Middle East war, and don't want another. They no longer believe in cakewalks. They're starting to grasp that countries don't like being invaded, even by Americans. Even before they witnessed a rebel leader taking a bite from the heart or some other internal organ of a Syrian government soldier, their hearts weren't in it. They are refighting the last war. Thank goodness.