(CNN) -- "We need long-term to take out ISIS' leadership, to degrade their operational capabilities, to cut off their financing sources, to go after them in a comprehensive way to cut off their ability to do the things we've seen them do."

Those were the words of State Department deputy spokeswoman Marie Harf on Monday -- suggesting the Obama Administration is preparing to do much more against the Islamic State in Syria and Iraq than deprive it of the Mosul Dam. They sounded much like the checklist used to degrade al Qaeda over a decade.

Until the sudden capture of Mosul in June, ISIS was of concern to Western governments but not a pressing priority. Since then, the threat to Baghdad, the plight of the Yazidi minority in northern Iraq, direct threats to U.S. interests and citizens and now the gruesome execution of American journalist James Foley have galvanized an unlikely coalition.

Iran, Saudi Arabia, the United States and Jabhat al Nusrah, the al Qaeda affiliate in Syria: all have the same adversary.

On Wednesday, President Obama said: "There has to be a common effort to extract this cancer so it does not spread." French President Francois Hollande concurs. In an interview with Le Monde Wednesday he called for a "comprehensive strategy against this structured group, which has access to substantial funding and to very sophisticated weapons, and which threatens countries such as Iraq, Syria or Lebanon."

The first step in taking down al Qaeda central was the invasion of Afghanistan to deprive it of living space. This time, the United States hopes others -- specifically the Kurdish Peshmerga and Iraqi armed forces -- will do that part of the job against ISIS, with a little help from U.S. drones and F-16s.

Even so, killing off an organization that is now much more potent than al Qaeda or its affiliates will depend on a lot of things going right in a region where much has gone wrong.

Here are just a few of the challenges.

1. ISIS has considerable territory

In eight months, ISIS has taken control of swathes of western and northern Iraq, and expanded its presence in northern Syria. For hundreds of miles along the Euphrates and Tigris rivers, ISIS is the power in the land; it now holds an area larger than the neighboring state of Jordan. While al Qaeda never really held territory beyond training camps and caves in remote parts of Afghanistan, ISIS controls cities (Mosul, Tikrit and Tal Afar in Iraq; Raqqa in Syria) and oil fields, main roads and border crossings. And it possesses more military hardware than some national armies after seizing both Iraqi and Syrian military bases and armories.

Critically, ISIS is able to use both Syrian and Iraqi soil in a much more muscular way than al Qaeda and the Taliban used the mountain tracks between Pakistan and Afghanistan. This gives it tactical flexibility and safe havens. Although its Syrian strongholds have come under aerial attack recently by the Syrian air force, the group retains control of Raqqa and Deir Ezzour provinces in the north and east of the country, and has in recent days seized villages close to Aleppo, some 250 miles from the border with Iraq. It also holds villages and towns along the Syrian border with Turkey.

As ISIS threatens to overwhelm other rebel groups (see below), especially the remnants of the Free Syrian Army, one critical factor will be the Syrian regime's tactics. Until recently it has focused its fire on other groups in securing Damascus and retaking Homs. There are signs it now sees ISIS as a clear and present danger; ISIS has seized several military bases in Raqqa province, and threatens to take the important Tabqa air base.

In the last week, the Assad regime has stepped up its use of air-strikes against ISIS, no doubt aware of the coincidental benefit of showing the West that Syrian help is required to tackle ISIS.

ISIS could be squeezed from several directions, but it would require co-ordinated commitment from Syria -- which has other battles to fight and may still see ISIS as a useful counterbalance against other rebel groups -- as well as the Iraqi army and the Kurds. Desperation has led Baghdad to co-operate with the Kurds. Whether that is sustainable is open to question.

2. ISIS has men, money, munitions

Unlike most jihadist groups, ISIS has some serious weaponry and plenty of seasoned fighters. In an assault on a major Syrian army base earlier this month, ISIS deployed three suicide bombers and dozens of well-armed fighters. A long battle ended with the fall of the base (one of the last held by the regime in Raqqa) and -- according to Syrian activists -- the summary execution of dozens of soldiers.

It was symbolic of ISIS' ability to conduct complex operations simultaneously in theaters hundreds of miles apart. The Syrian Observatory for Human Rights claims ISIS gained 6,300 new recruits -- 80 percent of them Syrian and the rest foreign -- in July alone. While U.S. officials say the number of active fighters probably numbers some 15,000, Iraqi analysts believe ISIS may be able to field three times that number.

A significant number are from Europe, Australia and the former Soviet Union. On Wednesday, Austrian prosecutors said nine people had been arrested on suspicion of intending to join Islamic militants in Syria, the latest indication of the stream of radicalized young Muslims lured to the promised land.

ISIS paints a picture of this land through a sophisticated outreach program on social media and through its English-language online publication, Dabiq, which is full of accounts of the coming showdown with "crusader armies," appeals to Muslims to come to the Islamic State and promises that "it is only a matter of time and patience before it reaches Palestine to fight the barbaric jews."

The aim of creating a Caliphate gives the group a mission that appeals to many young jihadists in Syria, Iraq and beyond. It's a goal that gives ISIS' campaign religious underpinning, and is constantly referred to in the group's literature.

ISIS has shown a ruthless discipline in its military tactics, forcing the Iraqi military to fight on several fronts at once and using mobile groups of a few dozen fighters as a first wave in attacking targets. It has a well-deserved reputation for accepting casualties in the pursuit of an objective and uses probing operations to test defenses (as in Mosul) and to keep opponents off-balance. In July, ISIS fighters attacked gas installations in Homs province, which diverted Syrian forces, only to then launch more concerted assaults on targets further east.

According to the Institute for the Study of War (ISW), which follows ISIS' campaign closely, "the breadth of these linked offensives across Iraq and Syria illustrate the ISIS priority objective of establishing territorial integrity for the Caliphate, and are evidence of the large military capacity ISIS still possesses nearly two months after the fall of Mosul.

"As continued military successes from increasingly unified theatres of operation fuel the ISIS war machine, a hardened ISIS exterior line is likely to allow ISIS forces to pursue further expansion," ISW says.

ISIS control of border crossings is a source of revenue, as are bank raids in the towns and cities they have seized. The group has seized oil refineries, and may make as much as $2 million a day from its control of fuel supplies in northern Iraq. They also hold the al-Omar oilfield in Raqqa.

3. ISIS is strangling the Syrian rebels

Perhaps the most immediate -- and most difficult --- challenge in reversing the ISIS tide is preventing it from killing off what remains of the more moderate Syrian opposition to Bashar al Assad. Already driven out of Homs through starvation, these groups are now caught between the hammer of ISIS and the anvil of the Syrian army in and around Aleppo. ISIS is closing in on Aleppo from the north, while the regime cuts off other routes.

Brian Fishman, who has followed the rise of ISIS longer than most, says that supporting the Free Syrian Army earlier might have blunted ISIS, "but that's a pretty hollow position if one also gives Syrian rebel factions a pass for tolerating and even embracing ISIL and Jabhat al-Nusrah through late 2012."

The remnants of the Free Syrian Army are disjointed and deflated -- and deeply resentful of failed western promises to provide the sort of military aid that would have tipped the military balance. Elements of the anti-ISIS Islamic Front are also starved of resources, and even Jabhat al Nusrah, the al Qaeda affiliate in Syria, has shifted its focus rather than take on ISIS.

After its gains north of Aleppo, ISIS may also be able to extend its control to parts of the Syrian-Turkish border, cutting off resupply routes for other groups. Syrian activists say ISIS fighters are now just a few miles from the town of Azaz, close to the border.

Can the U.S. and its partners help revive Syrian rebels to the point they can take on ISIS before the military balance in Syria tips decisively against them?

The record is not encouraging. Exactly three years ago, President Obama said the United States would lead the effort in "pressuring President Assad to get out of the way of this [democratic] transition, and standing up for the universal rights of the Syrian people - along with others in the international community."

Assad is still standing. The rebels are in disarray. And the Syrian people can only imagine what universal rights might look like.

4. ISIS hasn't over-reached as yet. But there are signs

Much of ISIS' success has derived from its ability to strike local deals with Sunni tribes in both Syria and Iraq -- either in the face of a common enemy or because tribal leaders see opposition as futile and/or suicidal. In Syria, for example, ISIS commanders co-opted the Sharabia tribe in joint operations against local Kurds.

It has shown merciless cruelty to enemies, beheading Syrian soldiers and executing Shia civilians and soldiers in Iraq. Displaying severed heads and other draconian demonstrations of ruthlessness are calculated to create a climate of fear among would-be adversaries. Human Rights Watch noted reports this week that ISIS had "executed as many as 700 members of the Sheitaat tribe in Deir al-Zour governorate, many of them civilians."

This ruthlessness is the ultimate form of totalitarian control -- but controlling such a vast area is only possible with the acquiescence of the civilian population. And this may change, especially if the new Iraqi Prime Minister extends an olive branch to the Sunni tribes; and if those who would oppose ISIS, both in Iraq and Syria, get support in the form of intelligence and weapons and support from the air.

Dawn Chatty, a social anthropologist at Oxford University, says that in north-eastern Syria "the Bedouin are very hard to terrorize, and the Bedouin will really come back." The head of the Sheitaat tribe has already called on other groups to join it in opposing ISIS.

But ISIS has shown itself to be smarter than its equally ruthless predecessor, al Qaeda in Iraq, which ultimately alienated Sunni tribes and led them to sign up for the U.S.-sponsored "Awakening" against extremism. It has provided food, fuel and security to populations on the brink of destitution after three years of civil war in Syria. And as Yochi Dreazen notes in Foreign Policy, ISIS "has generally allowed the local bureaucrats in charge of hospitals, law enforcement, trash pickup, and other municipal services to stay in their jobs." Its sharia courts have cut crime -- albeit more by cruel example than by due process.

While Raqqa is the flagship of ISIS' model of governance, there are other Syrian towns -- such as al-Bab and Manbij -- where it has shown organizational skills. Charles Caris at the Institute for the Study of War says that "as ISIS takes sole control over territory, it expands to provide more services, often operating the heavy equipment needed to repair sewer and electricity lines."

But running towns and dispensing services is a costly business, and there are only so many banks to empty. As Caris observes: "The immediate provision of aid and electricity, for example, does not translate into the creation of a durable economy."

5. The Iraqi government still needs to get its act together

In some ways, Iraqi Prime Minister Nouri al Maliki was the best recruiting sergeant ISIS could wish for, repeatedly alienating the Sunni minority with heavy-handed tactics against dissent, followed by indiscriminate bombing when ISIS took Fallujah in January. Maliki became identified with a chauvinistic Shia outlook heavily influenced by Iran.

Now Haidar al-Abadi -- the Prime Minister in waiting -- has the opportunity to win back the support of senior military commanders who had become disillusioned with the way Iraq's security forces had been so brazenly politicized, and lure the Sunni tribes back into political process. And that would starve ISIS of the "host" on which it has thrived for the past few months.

Some Sunni tribal leaders have already make it clear they will deal with al-Abadi, if the price is right. Iraqi analysts say this price includes an end to the allocation of ministries and other arms of government purely on the basis of partisan patronage.

The Kurds seem ready to give al-Abadi a chance. Hoshyar Zebari has returned to his post as Iraqi Foreign Minister in Baghdad, telling CNN's Becky Anderson Wednesday: "We've rejoined the caretaker government."

After the recapture of the Mosul Dam, the Iraqi army has launched another attempt to retake Tikrit. But so far ISIS is still in control of most of the town. There is a long way to go before real progress against ISIS can be demonstrated.

6. The international coalition needs to stick together

The events of the last few weeks, especially the horrendous brutality of ISIS that has mobilized global opinion and the existential threat to Iraq as a state, has concentrated minds from the Gulf to Europe and Washington.

"Suddenly, a common enemy has joined mutually distrustful players in the making of a coalition against ISIS -- just the kind of multilateralism that the U.S. President favors," writes George Packer in The New Yorker.

But does that coalition have willpower and cohesion to pursue what will be a costly -- and long-term -- mission? Will the U.S. be ready to use greater military force in Iraq in support of both the Kurds and the Iraqi military, including the deployment of Special Forces, given that the Obama administration sees ending the war in Iraq as a major achievement? And will the new government in Baghdad -- still likely to be a largely Shia coalition -- make enough concessions to both the Kurds and Sunnis to rekindle the 'concept' of Iraq?

In Syria, will the friends of the opposition, including the U.S., Turkey and the Gulf states be ready to prioritize the goal of helping rebel groups, including even Islamist elements, against ISIS, over the long-term aim of removing al Assad? Time is short.

Frederic Hoff of the Atlantic Council argues that "if, for example, the [opposition] Coalition were to establish itself in northern Syria, its associated military elements would need -- among other things -- the means to neutralize regime military aviation and ISIS ground forces." That's a lot of means.

Some former US military officials have spoken of the need to put 10,000 to 15,000 US troops on the ground to "roll back" ISIS. Brian Fishman, a Fellow at the New America Foundation, writes in War On the Rocks that "10,000-15,000 troops vastly understates the true commitment, which will actually require years, direct military action on both sides of the Iraq/Syria border, tens (if not hundreds) of billions of dollars, and many more than 15,000 troops."

And Fishman takes a pessimistic view of the prospects of getting rid of ISIS any time soon.

"The political consensus to incur the risks and costs of destroying ISIS is tremendously unlikely. And even then, success hinges on dramatic political shifts in both Iraq and Syria that under the best of circumstances will require years."

Which is where we started: the "long-term." And even then.