FIFTY years ago, President Lyndon B. Johnson authorized a strategic bombing campaign against targets in North Vietnam, an escalation of the conflict in Southeast Asia that was swiftly followed by the deployment of American ground troops. Last month, President Obama expanded a strategic bombing campaign against Islamic insurgents in the Middle East, escalating the attack beyond Iraq into Syria.

Will Mr. Obama repeat history and commit ground troops? Many analysts believe so, and top officials are calling for it. But the president has expressed skepticism about what American force can accomplish in this kind of struggle, and he has resisted the urgings of hawks inside and outside the administration who want him to go in deeper. Mr. Obama, his supporters say, is a “gloomy realist” who has learned history’s lesson: that American military power, no matter how great in relative terms, is ultimately of limited utility in conflicts that are, at their root, political or ideological in nature.

It’s a powerful, reasoned position, amply supported by the history of America’s involvement in Vietnam. But that history also shows that a president’s attitude and analytical assessment, no matter how gloomily realistic, are not necessarily an antidote to ill-advised military action. Foreign intervention has a logic all to itself.

Today we think of Lyndon Johnson as a man unwaveringly committed to prevailing in Vietnam. But at least at first, he shared Mr. Obama’s pessimism. He and his advisers knew they faced an immense challenge in attempting to suppress the insurgency in South Vietnam. “A man can fight if he can see daylight down the road somewhere,” he said privately in early March 1965. “But there ain’t no daylight in Vietnam.”

Johnson also knew that the Democratic leadership in the Senate shared his misgivings, and that key allied governments counseled against escalation and in favor of a political solution...