Basically that line is just filled by repeating the phrase for reasons of rhythm and emphasis. You must remember that "doing the laundry" (in the sense of cleaning away the Germans) is the topic of the song and that "Waschtag" has the figurative meaning of "the day when all scores will be settled, all unfinished business will be cleaned up, the day of retribution" in German. See this newspaper article for a contemporary use of the word. The "ja" between the two repetitions is a typical connector between such repetitions in songs in German and only adds emphasis, although you might spell out this emphasis as "indeed" or "make sure to":
Sing this song ...
until washing day, indeed make sure you sing it until washing day.
In English songs "yes", "yeah", "come on" and similar fillers have the same function.