As the Isis onslaught continues inside Iraq, in America Republican critics are laying the blame firmly with President Barack Obama.

Iraq's spiralling violence, they contend, is the direct result of two key Obama mistakes.

Firstly, his decision not to leave a US force in Iraq after the formal military withdrawal in December 2011. Leaving a residual force, they argue, would have ensured the continuity of Iraq's security.

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Secondly, his refusal to sanction military action against the Syrian regime in 2013, and to arm "moderate" Syrian rebels. Taking these actions, it is contended, would effectively have stifled the Isis insurgency, nipping it in the bud.

Could Obama have done better? Perhaps, but it is worth bearing in mind that he won office in 2008 promising to end the costly US mission in Iraq and that this commitment was extremely popular. Any decision to leave a residual US force in Iraq beyond the designated exit deadline would have been castigated by many Americans.

It must also be acknowledged that maintaining a residual US military presence required the assent of the Iraqi government. But the Iraqi government rejected this proposal after Baghdad-Washington negotiations broke down over the issue of granting legal immunity to remaining US troops.

Perhaps Obama's critics think that this rejection should have been ignored by Washington but this would have been a deeply questionable stance to take against the democratically elected Iraqi government, supposedly a key US ally in the Middle East.

Critics' accusations that Obama "got it wrong" over Syria are also dubious. Support for US air strikes against Syria was never high amongst war-weary Americans; by September 2013, some polls showed just 20% support.

With political tensions in Washington running high due to the domestic fiscal crisis, Obama thought it prudent to seek a congressional resolution for possible air strikes. However, support for this option was lukewarm on Capitol Hill and against the backdrop of a UK parliamentary vote which effectively precluded any British involvement in Syria, Obama saved Congress from having to vote by ruling out direct action against Syria. In refusing to arm "moderate" Syrian rebels, Obama insisted that US weapons could easily end up in the hands of more radical elements.

Where his opponents cry "negligence", Obama's supporters could just as easily argue that his big decisions on Iraq and Syria were prudent. That things have subsequently gone so awry in Iraq may simply demonstrate one of the unchallengeable truisms of foreign policy-making: one can never see all outcomes and that good decisions can easily turn out to be bad.

Messrs Cheney, Graham, McCain, Wolfowitz, et al, do not see it thus. With the "right decisions", they argue, the President could have maintained greater control of the Middle East, using US military power. Obama's critical mistakes, they contend, were to withdraw prematurely from Iraq and to withhold the US from Syria altogether.

However, this viewpoint represents a familiar and dangerous strand of US foreign policy thinking: namely, that military means can bring about chosen political outcomes and head off all dangers. But, if the post-9/11 period demonstrates anything, it is surely that US militarism actually has little capacity to control the trajectory of international politics. It is certainly unable to facilitate Washington's desired outcomes across a dangerously complicated Middle East. Indeed, it is easy to point to the role that US military activity - both military action and military assistance - has played in nourishing those dangers and complications.

Precisely what US-led air strikes might have achieved in Syria is anyone's guess. Indeed had he ordered them, Obama could now be facing censure for having sanctioned an expensive air war which served only to further obliterate Syrian infrastructure and kill government soldiers, insurgents and civilians alike. And flooding the warzone with US weapons would also carry rather obvious risks.

Equally, there is no guarantee that leaving a residual US force in Iraq would have stopped the rise of Isis and its current offensive. If such a force had been left behind, it might now be involved in a bloody battle against Isis, leaving Obama facing the prospect of having to order a further military deployment to Iraq in order to support US troops.

Obama has always appeared mindful of the limitations of military force. Yet his preferred approach - military disengagement where possible, employing drones, an emphasis on diplomacy and international consensus - has not stopped Syria and Iraq descending into carnage. This has exposed him to criticism and yet the approach his critics say he should have adopted - maintaining a muscular military presence in the Middle East, intervening militarily where feasible and arming selected groups where it is not - has its own proven record of failure.

The current Isis onslaught thus represents a perplexing conundrum. With US drones already gathering intelligence over Iraq, Obama has announced that 300 Special Forces personnel will deploy to Iraq in order to assist the Iraqi government. Politically, this is a necessary commitment from Obama but it is unlikely to sway the course of the ground war. US air support may have more impact but its limitations are all too well-known.

It will greatly pain Obama to backtrack on his cherished wish to disengage from Iraq. He will also be aware of the risk attached to openly supporting a regime - that of Prime Minister Nouri al-Maliki - which has emerged as a divisive sectarian force inside Iraq.

The fact is that a clear and winning strategy does not exist for the US in Syria and Iraq. This does not reflect policy failure on the part of the Obama administration. Rather, it reflects a wider truth: that for all its superpower status, the US has very little control over the politics and conflicts of the Middle East.

Those in Washington who think otherwise, and who think that military power is the mechanism by which control can be attained, are wrong - dangerously so.