The Republican presidential candidates mentioned the Islamic State more than 100 times in their latest debate on Tuesday — twice as often as they brought up President Barack Obama, whose strategy to defeat the militant group, they all seemed to agree, was, in the words of New Jersey Governor Chris Christie, that of a "feckless weakling."

After the assaults in Paris and San Bernardino, with public fear of terror at its highest point since the days after the 9/11 attacks, discussion of the Islamic State (IS, also widely known as ISIS) — how to deal with it and who's at fault for its success — is now dominating the GOP primary.

But confusion over what Obama has done so far and about the factors constraining the government's range of options seemed to infect the entire debate.

"The policy positions were an amorphous abyss," remarked Clinton Watts, a former executive officer of the Combating Terrorism Center at West Point who is now a fellow at the Foreign Policy Research Institute. "I hate to say it, but they were saying some stupid things last night... and what wasn't stupid was mostly just a rehash of Obama's policies."

Though much misunderstood, the Obama administration's military strategy against IS is quite simple: the US military is backing armed groups on the ground, most notably the Kurds, and the CIA is training and equipping smaller Sunni Arab rebel forces. In September 2014 the US assembled a coalition of regional powers to bombard IS from the air, shying away from soft targets like oil infrastructure at first. In the two months that followed the Paris attacks, the coalition has adjusted its focus by striking oil trucks and wellheads in IS-controlled territory. So far, the US has flown over 9,000 bombing missions against IS targets.

During Tuesday's debate, frontrunner Donald Trump repeated his boast from the stump that he deserves credit for the idea of targeting IS oil assets.

"I've been talking about oil for three years," he crowed. "I've been saying, 'Take the oil, take the oil.' "

Trump also began to outline a plan to escalate the war on IS energy resources before he was cut short by CNN moderator Wolf Blitzer.

"I didn't say, 'just bomb it.' I said, 'Take it and use it and distribute it so that the wounded warriors…,'" Trump said, hinting at a policy of directing funds from Syrian oil to help wounded US veterans, though Blitzer kept him from elaborating.

Later, Trump defended his suggestion that the relatives of IS members be targeted for death in response to a question from a Georgia Tech student, who asked, "How would intentionally killing innocent civilians set us apart from ISIS?"

"I would be very, very firm with families," he insisted. "Frankly, that will make people think, because they may not care much about their lives, but they do care, believe it or not, about their families' lives."

His rivals all seemed to agree that the idea flirted with the limits of constitutionality. Jeb Bush said that it "lacked seriousness."

While the US has destroyed hundreds of fuel trucks and seriously disrupted the IS oil economy, the group continues to be well funded, since it brings in most of its cash from taxes and extortion. As VICE News has reported, civilians living under the insurgency's thumb feel the brunt of these oil strikes, as they nudge up fuel and food prices without seriously affecting IS's military capabilities.

Texas Senator Ted Cruz was particularly critical of Obama's bombing campaign, suggesting that the US should "carpet-bomb ISIS to oblivion." When asked by Blitzer how he would avoid civilian casualties, Cruz replied that he "would carpet bomb where ISIS is — not a city, but the location of the troops." He recommended that the US revive its strategy from the first Gulf War, when the military launched 1,100 strikes a day against Saddam Hussein's army.

"Proposing more bombings is like saying you want to send more emails… it's easy and painless," Watts said of Cruz's proposal. "But it's proven to not be very effective against ISIS." That's because, Watts explained, such a strategy completely misunderstands how the group operates. "They are housed within a civilian population," he said. "This is mostly a Toyota truck army — it's not the Iraqi Republican Guard."

It's impossible to deny that more than a year after Obama announced his intention to "degrade and eventually destroy" the group, progress against it has been slow. As Florida Senator Marco Rubio emphasized during the debate, IS affiliates have even managed to expand away from the central battleground in Iraq and Syria.

"This is a group that's growing in its governance of territory," Rubio said. "It's not just Iraq and Syria. They are now a predominant group in Libya. They are beginning to pop up in Afghanistan. They are increasingly involved now in attacks in Yemen. They have Jordan in their sights."

At the same time, for over a year, IS has manage to hold on to major cities in Iraq and Syria. But Kurdish forces in particular have proved themselves capable of retaking ground from IS — most notably the recapture of Sinjar last month. In Tuesday's debate, Ben Carson suggested repeating the Sinjar victory all over Iraq and Syria.

"As far as the command centers are concerned in Raqqa and to a lesser degree Mosul, cut those off. Do the same kind of thing that we did with Sinjar," he said. But so far, Kurdish fighters are unwilling and incapable of retaking major cities like Mosul and Raqqa, where they would be viewed as an invading force by the local Arab population. Mosul and Raqqa have never been within the Kurdish sphere of influence.

So while the US has killed major IS leaders, including the group's finance minister last week, and managed to modestly reduce its territorial holdings, the group is firmly entrenched. No military force has yet been capable of dislodging IS from its core centers of power.

That's why the US has being trying to push a parallel diplomatic effort to unify the rebels who are unaffiliated with al Qaeda or IS while bringing all of the foreign powers involved in Syria — including Russia and Iran — into a dialogue about how to forge an accord, so that eventually combined forces can effectively confront the group.

The diplomatic process is also a slog, however. Rebel groups range from secular nationalists to right-wing Islamic brigades, and any semblance of unity is tenuous. At the same time, the international powers intervening in Syria cannot agree on the future of its besieged president, Bashar al-Assad, whose crackdown on peaceful protests during the 2011 Arab Spring sparked the civil war that fueled the rise of IS in the first place.

There was no debate whatsoever about the diplomatic track during Tuesday's date, but all of the GOP candidates balked at potential cooperation between the US and Iran. Texas Senator Ted Cruz claimed that "Iran has declared war on us," while Rubio referred to the country as our "moral enemy." For his part, Ohio Governor John Kasich declared that "we want to prevent Iran being able to extend a Shia crescent all across the Middle East."

In late October, the US invited Iran to Vienna to participate in diplomatic talks to end the Syrian crisis. It was the first time that Iran was included in such discussions, although it has long been a major backer of Assad and a de facto US ally against IS in Iraq. Indeed, last spring Iranian-backed Shia militias led the charge against the IS stronghold of Tikrit, backed by US airstrikes, scoring one of the only major territorial victories against IS.

Several of the GOP candidates suggested that a full military invasion of Syria should also be on the table. Aside from South Carolina Senator Lindsey Graham, a long-shot candidate whose poll numbers weren't sufficient enough for him to participate in the latest debate, Rubio is the loudest proponent of that view.

IS "cannot just be defeated through air strikes," he said during Tuesday's' debate. "They must be defeated on the ground by a ground force. And that ground force must be primarily made up of Sunni Arabs themselves, Sunni Arabs that reject them ideologically and confront them militarily."

Rubio wants a coalition of regional powers to march on IS strongholds.

"They have as much invested in this as we do," he said, explaining why Arab nations would be motivated to get on board with such a plan. "In fact, more so, for it is the king of Saudi Arabia they want to behead first. It's the king of Jordan that they want to dethrone. It's the — they want to go into Egypt the way they've already gone into Libya."

Such a coalition already appears to be in the works. Last week, Saudi Arabia announced that it had formed a 34-nation Islamic anti-terror coalition to take the fight to IS. On Wednesday, however, Pakistan — one of the major players in the would-be coalition — stated that it had never been asked to participate and that it had only learned of it's role through the Saudi announcement.

Even if an Arab-centered anti-IS force could be assembled, Watts warns that it is perilous to encourage a massive foreign invasion of Syria, given the region's explosive sectarian tension.

"It could trigger a massive Sunni-Shia war region-wide," he said.

Over the course of the debate, many of the candidates also struggled with basic facts about the conflict. Christie got the name of the king of Jordan wrong, and misleadingly suggested that the US had invited Russia to bomb Syria. Former Hewlett-Packard CEO Carly Fiorina suggested that Obama fired three top generals who had actually resigned of their own accord. And Ben Carson said that the war-ravaged Hasakah region would be a safe place to house refugees.

In Watts's view, the confusion over how to tackle IS stems from a larger failure to define an end goal.

"If we want to destroy ISIS and have some chance of installing democracy in Syria, we will have to spend billions of dollars over a decade or more and lose thousands of troops," he said. "If we want to do something more modest, we are going to have to take a back seat and let things develop on the ground. But no one wants to talk about either of those options, not in either party."