President Obama and his Joint Chiefs chairman, Gen. Martin Dempsey, seem to be engaged in a policy tug of war over troops on the ground in Iraq. After telling Congress last week that he was considering, once again, the deployment of ground combat forces to assist in the battle against the Islamic State, Dempsey made a surprise visit to Iraq over the weekend to further assess the evolving American military strategy—despite adamant assurances from the White House that combat forces are off the table.

The tensions between Obama and his most senior general are reminiscent of what another president, John F. Kennedy, encountered more than 50 years ago in the early days of America’s involvement in Vietnam. Today as then, it appears the nation’s top military officials are seeking to box the president in to a commitment the White House is extremely reluctant to make.

For Kennedy, the problem of Vietnam was supposed to be resolved by his predecessor and by the partition of the country in 1954 into communist and non-communist spheres with Saigon secured by its own military forces. For Obama, the security of Iraq was supposed to be maintained by the creation of a viable army formed following his predecessor’s invasion of the country in 2003, facilitating an orderly American exit. Then as now, a prior solution to a messy geopolitical conflict did not cohere and the United States was forced to fashion a new strategy...