Rat's Ass

I was listening to Folk Radio on Live365 when the commercial broke through the Ethel Caffie-Austin's John the Revelator asking "What is the difference be you and the millions of millionaires out there?" at which point my brain screamed I don't give a rat's ass! The reason behind the reaction isn't my point, but it's because one, are there really MILLIONS of millionaires out there? and two, are you kidding? the difference between me and them is they have a lot of money! And my reaction of not caring is because they're going to feed me a line of BS about how I can be a millionaire too. The Bible warns us against "Get Rich Quick" Schemes. ANYWAY! My point is, why did I say I don't give a rat's ass! ? Where did this term come from? Can I logically conclude that giving a rat's ass means caring? Should I say that from now on when someone tells me how hard their week has been, should I say "Oh man, that sucks...I give a rat's ass" ? And why a rat's ass? Are the origins of this idiom based in truth? Is there some kind of ancient custom of people cutting the hind end of of a rat to show their benevolence to someone??? Why don't keep the custom going? There could be a special bin where biology majors toss "used" rats after dissecting them and they could sell them as Benevolence Rat's Asses.