But the goal won't be to topple the Assad government, even though Obama has wanted that outcome for more than two years. Instead, White House officials say, the goal will be more limited: deterrence. The strikes will be aimed primarily at deterring Assad from using chemical weapons again.
But there are other kinds of deterrence Obama is hoping for too.
He hopes to deter other adversaries, especially Iran, from concluding that he doesn't mean it when he proclaims a "red line," as he did on chemical weapons in Syria last year.
At home, the president wants to deter hawkish critics, led by Sen. John McCain (R-Ariz.), from pestering him to do even more.
And Obama hopes the military can design the strike in a way that will deter Assad from retaliating against U.S. forces or its allies in the Middle East.
That's a lot of deterrence for any one campaign of missile strikes to accomplish. Still, it's important to notice the larger potential goals that Obama hasn't embraced.
Not only is he not seeking to overthrow Assad's government or destroy his armed forces through U.S. military action, he's not even aiming to tip the balance on Syria's battlefields decisively toward the insurgency. In large part, that's because the rebels who are best organized to take advantage of a power vacuum at this point are allied with Al Qaeda, not with us.
McCain and other hawks have called on Obama to seize this moment, when much of the world is appalled by Assad's use of chemical weapons, to intervene more decisively. The hawks want Obama to back up his calls for Assad's fall with more direct support for the rebels, including continuous operations by U.S. aircraft (which is what the deceptively mild term "no-fly zone" means in practice).
But that would be a mistake. Chemical attacks are an outrage, but they're not sufficient grounds for the United States to go to war. If a no-fly zone was a bad idea last month, as military officers have argued, it's still a bad idea.
Obama needs to begin a national conversation about our interests in Syria, both to ensure that war-weary Americans understand the reasons a bombing campaign makes sense and to limit the pressure for escalation when the airstrikes don't end the war.
Obama made a start on that conversation in an interview with CNN last week, when he argued that chemical weapons attacks touched "core national interests" in a way that Syria's conflict had not before.
He said the United States has a strong interest in "making sure that weapons of mass destruction are not proliferating" and also "to protect our allies [and] our bases in the region."
Those things, he suggested, were worth fighting for. And though the United States has other goals in Syria, including the protection of civilians and Assad's fall, they don't rise to the level of core interests, and so are not worth going to war over.
But the president still needs to explain his larger strategy, and how a bombing operation is connected to it.
Administration officials insist that they do have a grand design in Syria, even if it hasn't been notably successful so far. The strategy, adopted this year after months of internal debate, is to train and equip moderate, pro-Western factions among the rebels, and hope they grow in effectiveness and influence.
The goal is to help those rebels tip the balance in their own favor, not only in the war against the Assad government but also within the opposition against factions allied with Al Qaeda.
The best-case scenario is that the government will grow weaker, the moderate rebels will grow stronger, and members of those two camps will agree to a truce leading to a new government.
But the moderates haven't grown strong enough to exert much weight yet, either on the battlefield or in political negotiations.
That means U.S. strategy, for now, is focused primarily on a narrower, less inspiring goal: preventing victory for either the Assad government or for the Al Qaeda camp. Deterrence, if you like.
As a result, Obama's immediate goal is to keep the crisis over chemical weapons limited, and to deter Assad from using them again. His medium-term goal is to keep the Syrian civil war within manageable bounds in hopes that the pro-Western rebels will gain strength.
It's not a promising picture. The war could continue for years, claiming more dead on all sides. And, in the end, the moderates may lose. But the alternatives all look worse. Deterrence may be the least bad option there is.