(CNN) "I will quickly and decisively bomb the hell out of ISIS, will rebuild our military and make it so strong no-one -- and I mean, no one -- will mess with us."

"I would bomb the s*** out of them."

"The attack on Mosul is turning out to be a total disaster. We gave them months of notice. US is looking so dumb."

These are three of President-elect Donald Trump's remarks made on the campaign trail criticizing the strategy for taking down ISIS and declaring bluntly how he'd change it.

Trump pledged in September that on his first day in office he would issue his generals with a simple instruction: "They will have 30 days to submit to the Oval Office a plan for soundly and quickly defeating ISIS."

His premise is that the US-led coalition simply isn't ruthless enough. In an interview with Fox News in September, Trump said: "We have to lead for a change because we are not knocking them. We're hitting them every once in a while, we're hitting them in certain places, we're being very gentle about it."

But promises made in the heat of a campaign are often tempered by reality later. The complexities of tackling ISIS in two countries amid an array of competing parties do not give themselves easily to campaign slogans.

As of November 2, the US and its coalition partners had conducted a total of 15,959 strikes (10,310 in Iraq and 5,649 conducted in Syria), according to figures from the coalition . There have also been hundreds of airstrikes against ISIS in Libya since August. US commanders insist the air campaign has been remorseless and aggressive, but also in accordance with international law, calibrated to avoid civilian casualties.

The role of an air campaign is to aid ground forces. Short of accepting far greater destruction to cities as well as amplifying civilian suffering and displacement, it's hard to see how more intense airstrikes, as Trump has suggested, would change the military balance overnight. To borrow the words of US General Wesley Clark about NATO's campaign to evict Serbian forces from Kosovo in 1997: "The air campaign was an effort to coerce, not to seize." But ISIS is not the sort of group that's easily coerced.

The Mosul challenge

In concert with allied ground forces in Iraq and Syria, the air campaign has helped shrink ISIS' territorial control drastically and cut its lines of communication. This year the "caliphate" has lost control of the Iraqi cities of Ramadi and Falluja but Mosul is different : larger, more densely populated and of much greater importance to ISIS as its spiritual capital.

Even so, ISIS undertook elaborate preparations to defend the city, and its determined resistance so far suggests the campaign will be measured in months, not weeks.

After relatively smooth approaches to Mosul, entering the city has posed new challenges for Iraqi Security Forces. Airstrikes are called in daily; there were ten on Sunday alone. And using air power is difficult in densely-populated areas, where vehicle suicide bombs surge out of side streets and buildings are booby-trapped. Some sources suggest that ISIS is even forcing civilians to drive around the city to confuse the enemy.

"If there were no civilians, we'd just burn it all," Iraqi Major-General Sami al-Aridhi told the Washington Post. Last week, Al-Aridhi said he had paused operations at one point because there were too many families in the streets.

Iraqi forces have a foothold in ten eastern districts of the city, but have sustained heavy -- if undisclosed -- casualties in the process. They are short of heavy armor and precision weapons, often suffer from poor communications and are vulnerable to ambush in tightly-packed neighborhoods. They have claimed to have a district or another under control, only for fighting to break out again.

The Iraqi government -- with the support of the coalition -- wants Mosul's civilians to stay in their homes, both to prevent a humanitarian catastrophe and to prevent ISIS from using them as human shields. But unless security comes soon they will opt to flee. ISIS is using random mortar fire to terrorize civilians in liberated neighborhoods. Tens of thousands of people in Mosul "lack access to water, food, electricity and basic health services," the Norwegian Refugee Council said on Sunday.

It appears likely that the battle for Mosul will be ongoing when Trump is inaugurated on January 20. Will he double down on the presence of US Special Forces around Mosul, and change their role from "advise and assist" to fully-fledged involvement in combat? Will he opt for more intense aerial bombardment to raze areas ahead of the advance of allied ground forces? Or both?

Taking Raqqa

Mosul is a straightforward equation of forces (Iraqi troops plus coalition vs. ISIS) compared to ousting ISIS from Raqqa, the group's administrative capital in Syria.

No fewer than three competing forces want to declare victory in Raqqa: the Syrian army backed by Russian air power and Iranian paramilitaries; rebel factions supported by Turkish air power and artillery, and a US-sponsored (loose) alliance of Kurdish and Arab groups called the Syrian Democratic Forces (SDF).

And they are as interested in fighting each other as they are in confronting ISIS. US airstrikes have intensified to help the SDF edge forward in the northern Raqqa countryside. But none are close to the city limits.

To Fred Hof at the Atlantic Council , it's possible that President Trump will allow Russia and Bashar al-Assad's regime to deal with ISIS (and a host of other groups) in Syria. According to a statement from the Kremlin on Monday, President Putin and President-elect Trump discussed "issues related to solving the crisis in Syria" during their post-election phone conversation.

JUST WATCHED Syria: The biggest issue for the next US president? Replay More Videos ... MUST WATCH Syria: The biggest issue for the next US president? 00:41

As a candidate, Hof says, Trump "was trying to project a message consistent with his perception that many in the American electorate are fed up with the Middle East and are quite prepared, at least in principle, to leave the region and its problems to others."

Any political solution in Syria will require dialogue with Russia, Turkey, the Assad regime among others. The last four years of negotiation have been a bitter, unrewarding slog. And US engagement will be needed in Iraq to try to prevent a repeat of the conditions that led to the incubation of ISIS, guiding Iraq away from the sectarianism that has plagued the post-Saddam years.

The home front

It might seem ironic that ISIS supporters online have welcomed Trump's election. But it fits the group's perception that a war of religions is at hand.

ISIS and al Qaeda alike will hope that the President-elect follows through on his most severe remarks about Muslims at home and abroad. It can only hope that a Trump presidency alienates more Muslims -- not just militant Islamists.

ISIS may be battered in its self-declared caliphate, but it still believes it can bring forward a global religious war. Its online magazine Dabiq last year declared that "Muslims in the West will soon find themselves between one of two choices."

An article called "The Extinction of the Grayzone" said the world was divided into two camps -- the camp of Islam (represented by ISIS) and the camp of unbelief. Muslims in the West must renounce moderate leaders as traitors, according to Dabiq.

ISIS wants what Murtaza Hussain calls "an escalating spiral of alienation, hatred and collective retribution" -- in which it can "pose as the only effective protector for increasingly beleaguered Western Muslims."

JUST WATCHED Iraq: The biggest issue for the next US president? Replay More Videos ... MUST WATCH Iraq: The biggest issue for the next US president? 00:55

Realities of the task ahead

At this stage it's very tough to predict how the Trump administration will execute its promise to exterminate ISIS, let alone its broader Middle East policy. The national security elite of the Republican Party largely disowned Trump during the campaign; it's still unclear who will fill the top national security posts in the new administration.

The President-elect has set a demanding agenda that embraces economic nationalism, a hard line on immigration and multilateral trade deals and swift victory against ISIS. His team will need to be quick learners in the machinery of government in order to execute these directives.

But as Secretary of State John Kerry put it last week: "The pace of events across the globe does not allow for time-outs."