Not that it doesn't make sense, but that's a new one on me. I've heard people say they "have the vapors".
The southern idioms police might have to put Rush on their watch list...
My grandmother would frequently put the back of her hand to her forehead and complain mightily about having the vapors. The posture was usually accompanied by shallow breathing while her other hand fanned her face rapidly. My dad (her son) would just roll his eyes and ignore her. She always seemed to be in good health to me whenever she got the vapors.
He's got the ailment ('the vapors') mixed up with the remedy - smelling salts. I think he means that if this keeps up, he'll swoon (faint, pass out, have the vapors) and then he'll NEED smelling salts to revive him! :-)
Of course, smelling salts put out quite a vapor of their own - it's really ammonia.