"Wheel" doesn't tape "a month's worth of shows" in two days. They tape a WEEK's worth in two days. Three one day, two the next. Although the show's air running time is about 20 minutes (minus most of the commercials and all the promos), it takes far longer than that from start to finish. Each complete game sequence takes longer than 20 minutes and has to be edited to fit. Sometimes, sequences have to be reshot for technical reasons, like if some equipment just refuses to work. Usually, if you watch the credits at the end, you'll see a notice that a portion of the game not affecting the outcome was edited.
Plus, there's the audience warmup, keeping the audience amused between tapings (there's potty breaks), getting everyone back in their seats - three shows can be a fairly long production day. Even with no changes to the set.
Not to belittle what Barker does, nor his approach to it. As he says, he's learned his one song and he sings it.
Michael