This has been brought up a lot before. Learn to use the search function.
Anyway, I'd also recommend The Fall of America series for a plausible exploration of this POD.
I remember that. Murray Turtledove did a great job on that.....although, sadly, the ending to the last book in the series was kind of a downer, though. By 1908, if I recall, the U.S. was besieged by rather severe political corruption & incompetence, the Klan basically ruled the Deep South(with only Louisiana and Florida excepted) from top to bottom, and the economy was on the verge of total collapse. Did I mention, too, that we'd tried to invade Mexico, only for us to narrowly lose and were forced to pack up and go home(and Mexico was weaker than the C.S.A., too)? By the end, you couldn't help but root for Eugene Debs and the rest of the Socialists, no matter how radical some of them may have been; the Republicans were mostly milquetoasts, the Northern Democrats were hopelessly inept, the Southern Democrats were thoroughly corrupt, and the Progressives had no ideas on how to fix the country's finances.
There was quite a bit of good fanfiction on the 'Net during the '90s, which explored several possible conclusions to it all; my favorite piece was "Red Dawn", in which the Socialists took over in in the Twenties, and rebuilt the U.S.(or at least, those areas that accepted Socialist rule, which most of the South and some of the western states didn't) in their image.....although with the Dixiecrats and other nasty reactionaries festering in the background; what they tried to pull just after the end of *WWII ITTL is utterly shocking, when you think about it; how about a foiled plot to detonate a radiological device in San Francisco, for starters? But after that, though, it took a much more pleasant turn.....
OOC: Thought I might expand on the book series, if you don't mind. Also included a shout-out to Jello_Biafra's work, as well.