President Obama declared victory Monday night for his limited military intervention in Libya. After just a week, he said, America has achieved its goal of preventing a slaughter of the rebels. So does that mean Obama is ready to provide similar U.S. military help to besieged protesters down the road in Bahrain, say, or Yemen or Syria?

The answer is probably not - and that was an important but unstated note of realism underlying his attempt to explain what has been a confusing Libya policy. Although Obama came around to supporting a "war of choice" to halt Moammar Gadhafi, sources make clear that he doesn't see the Libya intervention as a precedent for similar interventions elsewhere in the region.

Obama offered a formula that's similar to what I heard last week traveling with Defense Secretary Bob Gates: The United States should use military force unilaterally only when it involves core U.S. national interests; in other cases, such as Libya, the United States should act militarily only with the support of its allies. America won't act as the world's policeman, in other words. But it's ready to act as "police chief," in organizing international peacekeeping operations.

Here's how Obama put it in one of the speech's key passages: "American leadership is not simply a matter of going it alone and bearing all the burden ourselves. Real leadership creates the conditions and coalitions for others to step up as well."

The president doesn't want to articulate this as an "Obama doctrine" - partly, no doubt, to leave himself maximum wiggle room - but it's there for all to see. And if there's any doubt about its roots in Obama's larger intellectual framework, turn to Page 308 of his 2006 book, "The Audacity of Hope," where he makes that same distinction between "imminent" core threats that require a unilateral response and ones where a multilateral approach is preferable.

White House officials tried to explain the "what's next?" issues that Obama's speech only hinted at. The initial military phase of the Libya campaign will be followed by political and diplomatic efforts (and, unstated, intelligence activities) aimed at creating a coalition government that can run Libya after Gadhafi is gone. The president understands that this is a messy mission, but at least it's a mess where the United States will have company - with the United Nations and major European and Arab countries along for the bumpy ride.

Already, according to Deputy National Security Adviser Denis McDonough, the United States is in contact with rebels and potential "reconcilables" within the Gadhafi regime about framing a future government. The Libyan opposition is such a rag-tag group that the White House may actually welcome a little time to get to know the players better and help them create transitional governing structures.

Obama appears to be evolving a hybrid strategy, blending "realist" and "humanitarian interventionist" themes. Several weeks ago the administration seemed almost to be allying with Shiite protesters in Bahrain against the minority Sunni monarchy. But Obama has recognized that America has an abiding interest in the stability of neighboring Saudi Arabia, which sees Bahrain as its 51st state and won't tolerate the overthrow of its ruling family.

Sustaining counterterrorism policies

Similarly, in the case of Yemen, Obama is balancing America's enthusiasm for a democratic political change with its strategic need for a strong government that can combat al-Qaida's operations in the Arabian peninsula. President Ali Abdullah Saleh is on his way out, but the White House sensibly wants to have a better understanding of what's on the other side of this transition - and to make sure that counterterrorism policies will be sustained.

Obama's speech Monday was a lesson in how presidencies are a matter of trial and error. A candidate who came into office partly on the strength of his opposition to the Iraq War has ended up committing more American troops on more battlefields. Yet he does it, each time reluctantly, delaying and debating before sending the military.

Obama gave a good Libya speech, but soon he needs to deliver a "Cairo II" speech that will articulate a coherent strategy for the region. As he said, "history is on the move" from Morocco to Iran - and yes, in Afghanistan and Pakistan, too. If Obama can connect his AfPak policy with the democratic wave that transformed Tunisia and Egypt, he will solve the core riddle of his presidency.