Mr. Obama, who had said at the beginning of the meeting that he would make no immediate decisions, appeared skeptical. He cautioned against a “haphazard” plan to arm the rebels, and asked about tactics — who would get the weapons, how to keep them out of the hands of jihadists.

The president’s view, according to one administration official who, like others, spoke on the condition of anonymity because he was discussing debates about classified operations, seemed to be that “we’d be taking a lot of risk without a clear plan.”

Fears of a Quagmire

For Mr. Obama, the Libya precedent loomed heavily over the Syria debate. That intervention in 2011 was strictly limited in scale and scope, and had the legal imprimatur of the United Nations Security Council as well as regional and international support. Even so, the Libya campaign had dragged on for seven months and expanded from protecting civilians to engineering the ouster of Colonel Qaddafi. Mr. Obama raised Libya repeatedly in debates as an example of how difficult it would be to prevent “mission creep,” if the United States were to cross the line to military operations.

As the president and his advisers debated their options in Syria, two American allies, Qatar and Saudi Arabia, were steadily funneling money and weapons to the rebels — and urging the Obama administration to join them.

But at the State Department, some officials were fuming about what they felt was a broken process and a lack of strategy.

The administration took more than a year to nominate a replacement for Jeffrey D. Feltman, a veteran Arabic-speaking diplomat who had coordinated the State Department’s Middle East policy and left in June 2012 for a job at the United Nations. Much of the department’s time was now being devoted to what was called the “post-Assad project,” the planning for political transition in Syria. Many State Department officials began to dismiss the project as a useless academic exercise. They believed that its premise — that Mr. Assad’s government was on the verge of collapse — was becoming outdated.

After Mr. Obama’s sweeping re-election victory, some of those officials, and others in the administration, expected a change in the White House’s position on Syria — and an end to what they saw as the stalemate of the previous year. Those expectations, however, were dashed during a meeting in early December. Michael J. Morell, who had taken over at the C.I.A. when Mr. Petraeus resigned after acknowledging an extramarital affair, renewed his predecessor’s pitch to begin arming the rebels. The agency had tinkered with the proposal made by Mr. Petraeus, partly to address directly the president’s skepticism about the plan.