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The State Department is now deploying government contractors to help the new Libyan government track down weapons.

Mr. Obama and his team say there is no Libyan doctrine that could be applied to other cases, though at the Pentagon, Defense Secretary Leon E. Panetta said Tuesday that NATO already has begun discussing how the Libya model might influence future operations.

Mr. Obama, speaking at a U.N. meeting on Libya, focused on the international community’s response.

“We are forever haunted by the atrocities that we did not prevent, and the lives that we did not save. But this time was different. This time, we, through the United Nations, found the courage and the collective will to act,” he said.

Danielle Pletka, vice president for foreign and defense policy studies at AEI, said U.S. policy could have been more forceful at the beginning, which she said could have sped Col. Gadhafi’s exit. Instead, she said Mr. Obama benefited more from “dumb luck” than a coherent policy.

“The key question any time you look at a foreign policy success or failure is you ask yourself, is this rooted in policy and principle, or is this just dumb luck. And if the answer is the latter, that tells you nothing about the president, nothing about his leadership and nothing about what will happen going forward. That’s the problem with Obama,” she said.

Lawmakers who opposed the operation altogether said they, too, are confused about what sort of precedent has been set. Some on both sides have argued — not all of them approvingly — that the Libya model could shape U.S. policy toward Syria, where protesters are endangered by government forces.

Mr. Kucinich said he’s already seen signs of expansion of U.S. policy, pointing to a debate within the administration over whether American forces can direct lethal force at rank-and-file militants in places such as Yemen and Somalia, where the U.S. is not at war but where it has an interest in the outcome of internal conflicts. The debate was reported last week in the New York Times.

Meanwhile, the court case challenging the president’s war powers is still proceeding, said Jonathan Turley, the law professor at George Washington University who is heading the legal effort.

In the past, courts have dismissed similar lawsuits when the underlying conflict was resolved, but Mr. Turley said he hopes the judge in this case will let the matter proceed. He said it’s time the courts provide some guidance on the issue, particularly since the same justifications for action in Libya could be used to intervene in other places such as Syria.

“We have committed to litigating this question as long and as far as necessary to fight for access to the federal courts,” Mr. Turley said.