two and barbecue other. in the phrase go two and barbecue, to be defeated in the first two games of a double-elimination tournament. (source: Double-Tongued Dictionary)
Further reading
Jim in Columbia, South Carolina, has noticed sportscasters’ use of the phrase on the season with reference to a period of time. This construction shows up in the sports pages as early as the 1880s, first referring to a team’s revenue and...
The slang phrase someone ate and left no crumbs means the person did something really well. In a previous call, a listener who works in theater noted the use of ate to mean “did something well,” as in they really ate that haircut! This...
Perhaps an extension of the single-elimination version one and done?
Many recipes for BBQ involve cooking the meat twice. For example steaming the meat first to tenderize it before further “flavor cooking” over a flame.
Perhaps that could have something to do with its origin.