Answer: Laryngitis
This conversation is between the host of the Texarkana tour and June before they introduce Johnny Cash and the Tennessee Two. She says this just to make the audience laugh whilst Johnny Cash and his band were preparing. As she is a comedienne, the audience sees June as the funny one of the Carter family, so comedy comes naturally on stage. After this conversation is over, we see Johnny backstage chuckling.
June Carter: "I gotta tell you, I can't sing tonight. I got the laryngitis."
[Crowd laughs]
June Carter: "Y'all laughin, but I do."
Billy: "We just heard you hollerin up a storm back there."
June Carter: "Well, I didn't have it then, Billy."