CNN has released a poll, conducted Friday through Sunday, that asked people for their views on President Obama’s handling of Libya. Initial reactions are more favorable for Mr. Obama than not, but the numbers are close enough that one can easily imagine some political downside for the president.

There are several different questions in the poll. For instance, when CNN asked people about the establishment of a “no-fly zone”, and provided a fairly lengthy description of it, support registered 70 percent, up significantly from last week. But support dropped to 54 percent when CNN asked a more targeted question about about airborne attacks on Muammar el-Qaddafi’s forces. And there was strong opposition to any use of ground troops, which president Obama has pledged not to employ.

I would caution, however, against interpreting these results overly literally. Some questions use relatively technical jargon like “no-fly zone”; others ask about hypotheticals, which are notoriously difficult to poll. Still other questions in the CNN poll ask about the “importance” of achieving various objectives, like removing Mr. el-Qaddafi from power, but the scholarly research suggests that “importance” is a relatively abstract concept that tends not to make for highly useful survey questions.

Probably the most relevant question, rather, is the first one that CNN asks: whether people approve or disapprove of Obama’s handling of Libya overall. This simply asks for a thumbs-up or thumbs-down based on the facts as people understand them in practice.

On that question, Mr. Obama registered 50 percent approval against 41 percent disapproval. That’s not substantially different from his overall numbers; in Gallup polling last week, for instance, Mr. Obama’s approval rating averaged 48 percent.

Support for Mr. Obama on the Libya question is a little bit less partisan than his overall numbers. For instance, 27 percent of Republicans support his actions in Libya thus far, as compared to the 15 percent who approve of his performance overall in Gallup polling. But Mr. Obama’s approval on Libya is 73 percent among Democrats, as compared to 81 percent overall. (Then again, one could be surprised that there is not more partisan mixing, since Democrats traditionally take more dovish positions and conservatives more hawkish ones.)

Despite these initial readings being decent for Mr. Obama, I would argue that these are not terrific numbers for him for a couple of reasons.

First, support for military interventions tend to be highest at the outset — the so-called rally-around-the-flag-effect — before declining until and unless some concrete objective is achieved. An important caveat is that the Libyan situation has evolved so quickly that we may still be midway through the rally phase. But if 50 percent approval is as good as the numbers get for Mr. Obama at the peak, overall support may turn negative unless Mr. el-Qaddafi is ousted fairly quickly.

Second, and this is a bit of an educated guess, but I suspect that Mr. Obama is more susceptible to a decline in support from liberals and Democrats on this question than he is likely to benefit from an increase in support among Republicans and conservatives. Reactions from prominent left-leaning bloggers and editors, like Josh Marshall, have been cautious — but generally skeptical and pessimistic. Some liberals, also, are not opposed to the action in Libya per se, but dislike the fact that Mr. Obama did not consult Congress before agreeing to participate in the allied action. (Some conservatives, undoubtedly, are in this camp as well.)

Finally, some of the scholarship suggests that support for military actions tends to be more tentative when the public is fatigued by other foreign entanglements, as they may be on Iraq and Afghanistan. Although they haven’t received much attention, recent polls suggest that Americans are growing continually more skeptical of the war effort in Afghanistan, with as much as a 2:1 majority concluding that the war is no longer worth fighting.