Boy, this is an old expression. I've often wondered what the origin is. In this context, we would not use "second" or "fourth."
It's basically a grilling, or an interrogation.
I think it's basically intended to be a "strong" interrogation, but it's often used as in your example, with a bit of sarcasm.
I've speculated in the past that it refers to the degrees in secret orders, like The Masons. Members advance in the order by "going through the degrees," or "going through the chairs." I think a senior member "gives them the degree" in the sense of testing whether they are worthy, according to some standard ritual, or something like that.
I'm sure Mrs. Google knows the answer.