For several years, President Barack Obama has operated under a set of assumptions about the Middle East: First, there could be no return of U.S. ground troops in sizable numbers to the region; and second, undergirding the first, the U.S. has no interests in the region great enough to justify such a renewed commitment. The crises in the Middle East could be kept localized. There might be bloodshed and violence—even mass killing, in Syria and Libya and elsewhere, and some instability in Iraq—but the fighting, and its consequences, could be contained. The core elements of the world order would not be affected, and America’s own interests would not be directly threatened so long as good intelligence and well-placed drone strikes prevented terrorist attacks on U.S. soil. Even Islamic State could be “degraded” and “contained” over time.

These assumptions could have been right—other conflicts in the Middle East have remained local—but they have proven to be wrong. The combined crises of Syria, Iraq and Islamic State have not been contained. Islamic State itself has proven both durable and capable, as the attacks in Paris showed. The Syrian conflict, with its exodus of refugees, is destabilizing Lebanon and Jordan and has put added pressure on Turkey’s already tenuous democracy. It has exacerbated the acute conflict between Sunnis and Shiites across the region.

The multisided war in the Middle East has now ceased to be a strictly Middle Eastern problem. It has become a European problem as well. The flood of refugees from the violence in Syria and the repression of Syrian President Bashar al-Assad’s regime have rocked the continent and overwhelmed its institutions. The horrific attacks in Paris, likely organized and directed by Islamic State from its base in Syria, and the prospect of more such attacks, threaten the cohesion of Europe, and with it the cohesion of the trans-Atlantic community, or what used to be known as the West. The crisis on the periphery, in short, has now spilled over into the core.

Europe was not in great shape before the refugee crisis and the terrorist attacks. The prolonged Eurozone crisis eroded the legitimacy of European political institutions and the centrist parties that run them, while weakening the economies of key European powers. The old troika—Britain, France and Germany—that used to provide leadership on the continent and with whom the U.S. worked most closely to set the global agenda is no more. Britain is a pale shadow of its former self. Once the indispensable partner for the U.S., influential in both Washington and Brussels, the mediator between America and Europe, Britain is now unmoored, drifting away from both. The Labor Party, once led by Tony Blair, is now headed by an anti-American pacifist, while the ruling Conservative government boasts of its “very special relationship” with China.

The spillover of the Middle East crisis into this weakened Europe threatens to undermine the continent’s cohesion and sap the strength of trans-Atlantic ties. The refugee crisis has further weakened centrist parties and strengthened the right wing in France and elsewhere; now the terrorist attacks, which these parties have unfairly linked to the refugee crisis, have given them a further boost. The idea of Marine Le Pen, leader of the right-wing National Front, as France’s next president is no longer far-fetched.

There is a Russian angle, too. Many of these parties, and even some mainstream political movements across the continent, are funded by Russia and make little secret of their affinity for Moscow. Thus Prime Minister Viktor Orban of Hungary has praised “illiberalism” and made common ideological cause with Russian President Vladimir Putin. In Germany, a whole class of businesspeople, politicians, and current and former government officials, led by former Chancellor Gerhard Schröder, presses constantly for normalized relations with Moscow. It sometimes seems, in Germany and perhaps in all of Europe, as if the only person standing in the way of full alliance with Russia is German Chancellor Angela Merkel.

Now the Syrian crisis has further bolstered Russia’s position. Although Europeans generally share Washington’s discomfort with Moscow’s support for Mr. Assad and Russia’s bombing of moderate Syrian rebels, in the wake of the Paris attacks, any plausible partner in the fight against Islamic State seems worth enlisting. In France, former President Nicolas Sarkozy has long been an advocate for Russia, but now his calls for partnership with Moscow are echoed by President François Hollande, who seeks a “grand coalition” with Russia to fight Islamic State.

Where does the U.S. fit into all this? The Europeans no longer know, any more than American allies in the Middle East do. Most Europeans still like Mr. Obama. After President George W. Bush and the Iraq war, Europeans have gotten the kind of American president they wanted. But in the current crisis, this new, more restrained and intensely cautious post-Iraq America has less to offer than the old superpower, with all its arrogance and belligerence.

The flip side of European pleasure at America’s newfound Venusian outlook is the perception, widely shared around the world, that the U.S. is a declining superpower, and that even if it is not objectively weaker than it once was, its leaders’ willingness to deploy power on behalf of its interests, and on behalf of the West, has greatly diminished. As former German Foreign Minister Joschka Fischer recently put it, the U.S. “quite obviously, is no longer willing—or able—to play its old role.”

Mr. Fischer was referring specifically to America’s role as the dominant power in the Middle East, but since the refugee crisis and the attacks in Paris, America’s unwillingness to play that role has reverberations and implications well beyond the Middle East. What the U.S. now does or doesn’t do in Syria will affect the future stability of Europe, the strength of trans-Atlantic relations and therefore the well-being of the liberal world order.

This is no doubt the last thing that Mr. Obama wants to hear, and possibly to believe. Certainly he would not deny that the stakes have gone up since the refugee crisis and especially since Paris. At the very least, Islamic State has proven both its desire and its ability to carry out massive, coordinated attacks in a major European city. It is not unthinkable that it could carry out a similar attack in an American city. This is new.

If, in addition to an increased threat to America, there is also a threat to the fundamental stability of Europe, does this not call for a reassessment of the policies that have so far been tried in Syria and Iraq? Those policies were based, in part, on a cost-benefit calculation: How much risk should be run, and how high a price should be paid, given the interests and the stakes involved? Now the interests and the stakes are higher than originally anticipated: The Middle East crises have metastasized and moved from what a cold, realist, interest-driven analysis might have described as peripheral parts of the body to its main organs. Have not events in the Middle East, and now in Europe, reached the point where significant interests are at stake, thereby requiring a more substantial response?

The French have already done that recalculation, at least in theory. Mr. Hollande has declared that France is “at war” with Islamic State. But with what capabilities—and indeed, with what will—can France and Europe fight this war? For almost two decades Europeans, and particularly Western Europeans, have chosen not to arm themselves sufficiently to fight a “war,” not only because they wanted to spend that money elsewhere but as a matter of philosophical conviction, derived from the bitter experience of the 20th century. Europeans believed that they, and eventually the world, had to move beyond power. Hard power had to give way to soft power, the rule of the jungle to the rule of law. This was the great philosophical gap that opened between Europe and the U.S., and never more glaringly than during the Iraq war.

In 2002, a British statesman-scholar issued a quiet warning. “The challenge to the postmodern world,” the diplomat Robert Cooper argued, was that while Europeans might operate within their borders as if power no longer mattered, in the world outside Europe, they needed to be prepared to use force just as in earlier eras. “Among ourselves, we keep the law, but when we are operating in the jungle, we must also use the laws of the jungle,” he wrote. Europeans didn’t heed this warning, or at least didn’t heed it sufficiently. They failed to arm themselves for the jungle, materially and spiritually, and now that the jungle has entered the European garden, they are at a loss.

With the exercise of power barely an option, despite what Mr. Hollande promises, Europeans are likely to feel their only choice is to build fences, both within Europe and along its periphery—even if in the process they destroy the very essence of the European project. It is this sentiment that has the Le Pens of Europe soaring in the polls.

The only alternative is to address the crisis in Syria and Iraq, and with it the terrorist threat posed by Islamic State. But just as in the 1990s, when Europeans could address the crisis in the Balkans only with the U.S. playing the dominant military role, so again America will have to take the lead, provide the troops, supply the bulk of the air power and pull together those willing and able to join the effort.

What would such an effort look like? First, it would require establishing a safe zone in Syria, providing the millions of would-be refugees still in the country a place to stay and the hundreds of thousands who have fled to Europe a place to which to return. To establish such a zone, American military officials estimate, would require not only U.S. air power but ground forces numbering up to 30,000. Once the safe zone was established, many of those troops could be replaced by forces from Europe, Turkey, Saudi Arabia and other Arab states, but the initial force would have to be largely American.

In addition, a further 10,000 to 20,000 U.S. troops would be required to uproot Islamic State from the haven it has created in Syria and to help local forces uproot it in Iraq. Many of those troops could then be replaced by NATO and other international forces to hold the territory and provide a safe zone for rebuilding the areas shattered by Islamic State rule.

At the same time, an internationally negotiated and blessed process of transition in Syria should take place, ushering the bloodstained Mr. Assad from power and establishing a new provisional government to hold nationwide elections. The heretofore immovable Mr. Assad would face an entirely new set of military facts on the ground, with the Syrian opposition now backed by U.S. forces and air power, the Syrian air force grounded and Russian bombing halted. Throughout the transition period, and probably beyond even the first rounds of elections, an international peacekeeping force—made up of French, Turkish, American and other NATO forces as well as Arab troops—would have to remain in Syria until a reasonable level of stability, security and inter-sectarian trust was achieved.

Is such a plan so unthinkable? In recent years, the mere mention of U.S. ground troops has been enough to stop any conversation. Americans, or at least the intelligentsia and political class, remain traumatized by Iraq, and all calculations about what to do in Syria have been driven by that trauma. Mr. Obama’s advisers have been reluctant to present him with options that include even smaller numbers of ground forces, assuming that he would reject them. And Mr. Obama has, in turn, rejected his advisers’ less ambitious proposals on the reasonable grounds that they would probably be insufficient.

This dynamic has kept the president sneering at those who have wanted to do more but have been reluctant to be honest about how much more. But it has also allowed him to be comfortable settling for minimal, pressure-relieving approaches that he must know cannot succeed but which at least have the virtue of avoiding the much larger commitment that he has so far refused to make.

The president has also been inclined to reject options that don’t promise to “solve” the problems of Syria, Iraq and the Middle East. He doesn’t want to send troops only to put “a lid on things.”

In this respect, he is entranced, like most Americans, by the image of the decisive engagement followed by the victorious return home. But that happy picture is a myth. Even after the iconic American victory in World War II, the U.S. didn’t come home. Keeping a lid on things is exactly what the U.S. has done these past 70 years. That is how the U.S. created this liberal world order.

In Asia, American forces have kept a lid on what had been, and would likely be again, a dangerous multisided conflict involving China, Japan, Korea, India and who knows who else. In Europe, American forces put a lid on what had been a chronic state of insecurity and war, making it possible to lay the foundations of the European Union. In the Balkans, the presence of U.S. and European troops has kept a lid on what had been an escalating cycle of ethnic conflict. In Libya, a similar international force, with even a small American contingent, could have kept the lid on that country’s boiling caldron, perhaps long enough to give a new, more inclusive government a chance.

Preserving a liberal world order and international security is all about placing lids on regions of turmoil. In any case, as my Brookings Institution colleague Thomas Wright observes, whether or not you want to keep a lid on something really ought to depend on what’s under the lid.

At practically any other time in the last 70 years, the idea of dispatching even 50,000 troops to fight an organization of Islamic State’s description would not have seemed too risky or too costly to most Americans. In 1990-91, President George H.W. Bush, now revered as a judicious and prudent leader, sent half a million troops across the globe to drive Iraq out of Kuwait, a country that not one American in a million could find on a map and which the U.S. had no obligation to defend. In 1989, he sent 30,000 troops to invade Panama to topple an illegitimate, drug-peddling dictator. During the Cold War, when presidents sent more than 300,000 troops to Korea and more than 500,000 troops to Vietnam, the idea of sending 50,000 troops to fight a large and virulently anti-American terrorist organization that had seized territory in the Middle East, and from that territory had already launched a murderous attack on a major Western city, would have seemed barely worth an argument.

Not today. Americans remain paralyzed by Iraq, Republicans almost as much as Democrats, and Mr. Obama is both the political beneficiary and the living symbol of this paralysis. Whether he has the desire or capacity to adjust to changing circumstances is an open question. Other presidents have—from Woodrow Wilson to Franklin Roosevelt to Bill Clinton—each of whom was forced to recalibrate what the loss or fracturing of Europe would mean to American interests. In Mr. Obama’s case, however, such a late-in-the-game recalculation seems less likely. He may be the first president since the end of World War II who simply doesn’t care what happens to Europe.

If so, it is, again, a great irony for Europe, and perhaps a tragic one. Having excoriated the U.S. for invading Iraq, Europeans played no small part in bringing on the crisis of confidence and conscience that today prevents Americans from doing what may be necessary to meet the Middle Eastern crisis that has Europe reeling. Perhaps there are Europeans today wishing that the U.S. will not compound its error of commission in Iraq by making an equally unfortunate error of omission in Syria. They can certainly hope.

Mr. Kagan is a senior fellow at the Brookings Institution and the author of “Of Paradise and Power: America and Europe in the New World Order” and, most recently, “The World America Made.”