You use the phrase ‘Till the Cows Come Home’ to indicate a period of time that is
both long and indefinite.
Example of use: “When will you be finished?” Answer: “I’m not sure. We’ll be working on this project till the cows come home.”
The origin of the phrase ‘til the cows come home’ comes from the practice of cows returning to their shelters at some indefinite point, usually at a slow, languid pace. The expression was in use during the 19th century, with an example appearing in print in 1829, in a British newspaper called The Times: “If the Duke will but do what he unquestionably can do, and propose a Catholic Bill with securities, he may be Minister, as they say in Scotland ‘until the cows come home.’”