With the shooting of Scalise, the phrase is starting to take on an entirely new meaning...but that is neither here nor there.
You just cannot make these things up. The irony? Mr. Gingrich's choice of words. Back in the nineteenth century, if you said "Indian Hunting Party," you might be understood to be referring to the parties organized by white pioneers, which offered hundreds of dollars for every "redskin" scalp, as a means of "exterminating the savages."
One has to admire the man, in some paltry degree, for this bit of revisionism-by-simile. This article includes an actual photo of a newspaper clipping, about such hunts for Native American Indians:
https://indiancountrymedianetwork.co...ooking-scalps/