A Vietnam Situation is akin to the Vietnam War in which the U.S. walked in expecting an easy victory and wound up spending years and lives in a costly war.
In slang a Vietnam situation is any sort of job or agreement one walks into and expects to be simple to complete but one finds out it will be quite time consuming and/or expensive.
Lately this slang has been synonymous with an Iraq Situation
Man, my grandmother wanted me to go under the house and see what was rattling around under there. I said 'Sure' I mean it was just a rattle. Turns out There's like fifty hornets nests down there and her sewage line has busted. We got a plumber out here and fourteen cans of pesticide. The whole thing is a Vietnam Situation.