At last the essential building blocks of a coalition against the ultra-violent criminal conspiracy that used to call itself the Islamic State of Iraq and Syria (ISIS) and now calls itself simply the Islamic State (IS) are falling into place. Everyone was caught off guard by their surge out of fairly remote areas of north and eastern Syria into western Iraq, and slow off the mark in responding. But with the United States having initiated airstrikes against the organization in Iraq – and having declared, in effect, a long-term war to destroy the organization’s capability to be a menace regionally and globally – the long-overdue effort to destroy these extremists is finally underway.

One of the most important recent developments is a massive shift in American public opinion, largely engineered by ISIS itself. By beheading two American journalists it was holding as hostages for ransom – James Foley and Steven Sotloff – and threatening to murder more Westerners in the event of additional American airstrikes, and, even more foolishly, by depicting these gruesome killings in Internet videos, the fanatics have roused the American public out of its war-weary risk-aversion.

The shift is nothing less than extraordinary. A Washington Post-ABC News poll suggests that 71% of Americans now favor air attacks against ISIS positions in Iraq, an increase of 17% over three weeks and 26% since mid-June. A majority still does not favor a ground intervention, but “boots on the ground” in any significant numbers are not required at this stage. Other opinion polls and surveys show a similarly dramatic shift in public opinion on the need for force against ISIS and the extent to which it’s recognized by the public as a significant threat to American interests.

Some observers have misinterpreted the ghastly ISIS beheading videos as a kind of provocation to the United States, hoping to elicit further airstrikes for reasons that are convoluted and difficult to explain. This is obviously incorrect. It’s quite clear, on the contrary, that ISIS fanatics were actually trying to use murder as leverage over Americans and their allies to dissuade them from further engagement.

It’s backfired spectacularly, of course, but it’s understandable how ISIS so badly misread the American mindset. For the past six years, dating back to a period in which ISIS itself did not exist except in the form of its precursor organization of Al Qaeda in Iraq (AQI), these fanatics have watched the United States draw down from conflicts in Iraq and Afghanistan and resist other provocations. They are used to the idea of an America that is backing, and perhaps in their own twisted thinking, running, away from Middle Eastern conflict.

What they failed to understand, it seems, is that what most Americans objected to was a war in Iraq that had no clear purpose and was a gigantic strategic miscalculation that cost their country enormously in terms of blood and treasure (not to mention international prestige) without yielding any clear gains. Indeed, many Americans now see the invasion of Iraq as a virtually unprecedented blunder, rivaled only by the extraordinary mistake of trying to seize control of Canada in 1812, only to have the British burn down most official buildings in Washington DC, including the White House.

But Americans don’t object to, and will support, a necessary campaign to break an extremist organization that is directly threatening their interests, murdering their compatriots and wreaking havoc in a region that is still essential to the United States. The much-ballyhooed “pivot to Asia” was always also implicitly a pivot away from the Middle East. Such a “pivot” never even began, and it isn’t going to in the foreseeable future, because, no matter how fed up and frustrated Americans have become with Middle Eastern conflicts given the Iraq fiasco, the Middle East remains essential to American national interests and a broad-based disengagement is simply not realistic.

International support for such a campaign is also clearly growing. British and American appeals to NATO allies last week reportedly met with a generally positive response. And support in the Middle East, particularly from the Arab allies of the United States, is obviously growing. The grand mufti of Saudi Arabia, Abdul Aziz al-Sheikh, recently declared: “The ideas of extremism, radicalism and terrorism … have nothing to do with Islam and (their proponents) are the enemy number one of Islam.” He specifically singled out ISIS as the primary example of this paramount enemy.

And in an extraordinary commentary article in the The Wall Street Journal, Yousef Al Otaiba, the UAE ambassador to the United States, issued what amounted to a declaration of war not only against ISIS, but against “radical Islam” in general. “Now is the time to act,” he wrote. “The international community needs an urgent, coordinated and sustained international effort to confront a threat that will, if unchecked, have global ramifications for decades to come.”

“The Islamic State may be the most obvious and dominant threat at present, but it is far from the only one,” Otaiba pointed out. He maintains that “an international response must confront dangerous Islamist extremists of all stripes across the region,” and called for a wide-ranging campaign of “direct intervention” to combat an “existential threat” from “the entire militant ideological and financial complex that is the lifeblood of extremism.”

This is by far the strongest, boldest and most far-reaching statement from a representative of any Arab government about what is at stake in the battle against ISIS and similar terrorists and extremists. There’s no doubt that the Ambassador is speaking on behalf of his government and, moreover, that although the UAE is taking a very public leadership role through such statements, its essential assessment is shared by a broader group of key Arab states that increasingly see an urgent need to combat violent extremism.

Meanwhile, the battle against ISIS will almost certainly continue to gain momentum. Tonight, US President Barack Obama will explain his strategy for dealing with these fanatics to the American public. While he’s likely to reassure them about “boots on the ground,” he’s also likely to stake out a strong position that ISIS must be destroyed, at least in the sense that it is rendered largely irrelevant.

Obama was elected president in the first place partly on the basis of his strong opposition to the Iraq war. He was right in this assessment, and also in his criticism of the prolonged nation-building folly in Afghanistan. And there was broad public support for his promise to end both campaigns, which he has indeed done. Some critics on the far left and right will no doubt claim that he is now leading the United States back into Iraq and resuming the conflict he promised, and was elected, to resolve.

Such critics can and should be prevented from making this specious claim, because while Obama was opposed to the war in Iraq, he was strongly supportive of the “war on terror,” which he specified as a war against Al Qaeda. And this is a war (of sorts) that his administration has pursued vigorously, most notably through covert actions and controversial drone strikes that have succeeded in killing terrorist leaders like Osama bin Laden and Anwar al-Awlaki.

Obama and his Administration can and should present the battle against ISIS not only as necessary and unavoidable, but also as a continuation of the war against Al Qaeda, since the group is a direct spinoff of the AQI. The battle against Al Qaeda was always Obama’s war, and it has now evolved into the struggle to defeat ISIS. Even with strong US public, international, and regional support, it may take time (the Obama administration is speaking in terms of three years or so) and require an intricate series of deft political and strategic maneuvers. But prevailing against the most dangerous group of extremists to have arisen in the Arab world in living memory is now both necessary and achievable.