I also recall another colloquial use of the word "Jack" ie: "Take your time, don't jack that up, we don't have another one" - that was used when we were working on cars in the garage.
But since you asked and made me curious... A little Googling indicates the "Jack-wagon" was the cowboy's chow wagon. That makes sense - if an errant cowboy required restraint out in the field, the chow wagon would be the logical place to put them. Or make them wash dishes / peel potatoes etc. for behavior modification.
Here's the definitions in the urban dictionary:
When something goes awry; someone who fouls something up, i.e., plans, projects, etc.
1. The vacation plans were jackwagoned.
2. I can't believe he messed up the vacation plans, what a jackwagon!
Jun 22, 2005
jackwaggon
A giant dumbass who doesnt know anything. Who would quite possibly get everyone killed because of his stupidity
man: bob what are you doing
bob: tryin to shoot that gas can
man: you damn jackwaggon
Oct 25, 2010
In fact there's a whole plethora of derogatory terms beginning with "Jack" listed, "Jackass", for example. But most of which are inappropriate in polite company.
I don't know who/what "Jack" was to deserve such a derogatory connotation - but he/it must have been of unsavory character, consistent with the degenerate character of those Jackweasels who wrote and signed the letter in the thread's subject article - and tried to "hiJack" the Tea Party into their Jack-wagon - which is loaded with a whole bunch of stupid, regardless of whether it's named Jack, or not.