A situation that is difficult to get out of. It is named after a type of wetland where if you walk through it, you will begin to sink.
In politics, it typically refers to a military action that is difficult to pull out of. Typically this is because leaving would create as many problems as it would solve.
The ‘quagmire theory’ is based on one of these situations: the Vietnam War. It is the theory that the US slowly waded into the war based on misinformation and false promises, and when they finally realized what they had gotten into, it was too late to get out safely.
Chicago Tribune: “The first step into a quagmire inexorably draws one down a slippery slope. [historian Arthur] Schlesinger argued that officials in the Kennedy and Johnson administrations stumbled blindly into Vietnam without understanding where the U.S. commitment would lead. Escalation proceeded through a series of small steps, none of which seemed terribly consequential. Each succeeding step was taken in the optimistic belief that a little more effort – a bit more aid, a few more troops, a slight intensification of the bombing – would turn things around by signaling American resolve to stay the course. Faced with this prospect, the reasoning went, the North Vietnamese communists would sue for peace on American terms. These flawed expectations, Schlesinger argued, arose from a decision-making system characterized by “ignorance, misjudgment and muddle.” A dysfunctional bureaucracy fed presidents misleading and overly rosy intelligence. The Vietnam War debacle, in other words, arose from inadvertence and folly.”