But she did not call for a change of direction.

Addressing an audience at the Council on Foreign Relations in New York, Mrs Clinton was in her element. The former Secretary of State and overwhelming frontrunner for the Democratic presidential nomination spoke confidently and in detail about a topic she knows more intimately than any other candidate from either party.

"It's time to begin a new phase to intensify and broaden our efforts, to smash the would-be caliphate and deny ISIS control of territory in Iraq and Syria," she said, referring to the Islamic State. "That starts with a more effective coalition air campaign, with more allied planes, more strikes and a broader target set." She also called for the creation of a no-fly zone to protect civilian Syrians.

Here you can see some differentiation from the Obama air strategy, which has been criticised by some military analysts as being too timid and too concerned with civilian casualties.

Mrs Clinton said Iraq's army needed to be expanded and reinvigorated to become an effective fighting force against IS, another element of the current US strategy.

But she went further, declaring that if the Iraqi government failed to arm Sunni and Kurdish militias fighting IS, then the US should arm them directly.

She called on Turkey to properly engage in the fight against IS.

"This is their fight, and they need to act like it," she said. "So far, however, Turkey has been more focused on the Kurds than on countering ISIS."

Mrs Clinton emphasised the importance of what she has long called "smart power" the co-ordinated deployment of all of America's levers of influence – "military and diplomacy, development and economic and cultural influence, technology and maybe most importantly our values" in a moral and military fight against IS.

And in keeping with the current administration's position, she dismissed out of hand the notion that America and the West was engaged in a clash of civilisations.

"Islam is not our adversary. Muslims are peaceful and tolerant people and have nothing whatsoever to do with terrorism," she said.

"The obsession in some quarters with a clash of civilisation, or repeating the specific words radical Islamic terrorism isn't just a distraction, it gives these criminals, these murderers more standing than they deserve. It actually plays into their hands by alienating partners we need by our side," she said.

Mrs Clinton's remarks did little to inspire hope that an administration lead by her had a strategy in place that might quickly lead to the end of Syria's bloody war, but they did suggest that she had some understanding of how infernally complicated the war has become.

This alone is enough to differentiate her position from some of her Republican rivals.

The two leaders of the Republican race have no political experience and no diplomatic experience, and it shows.

Explaining his plan last week billionaire property developer Donald Trump told a cheering campaign audience, "I would bomb the shit out of them.

 I would just bomb those suckers."

On Sunday - two days after the attack in Paris - the retired neurosurgeon Ben Carson appeared on Fox News to discuss foreign policy and said he would forge a coalition with America's traditional allies in the region to fight IS. Given three opportunities he could not name a single ally.

The Republican establishment's preferred candidate, Jeb Bush, made a foreign policy speech on Wednesday. He had more to offer.

Addressing cadets at the Military College of South Carolina, better known as The Citadel, Mr Bush trod the same path so many have before him.

"The United States should not delay in leading a global coalition to take out ISIS with overwhelming force," he said. "Militarily, we need to intensify our efforts in the air - and on the ground."

But he went further than Mrs Clinton, calling for US ground forces to be deployed, where she has only argued for an increased role for Special Forces.

How many he did not say.

He also deliberately cast the war with IS in the terms that the Republican mainstream now demands.

"We are at war with radical Islamic terrorism," Mr. Bush said.

"Radical Islamic terrorists have declared war on the Western world. Their aim is our total destruction. We can't withdraw from this threat, or negotiate with it. We have but one choice: to defeat it."