David bar Elias, I have looking back through this thread for references to Charles W. La Follette (a character whom I've been trying to flesh out for FILLING THE GAPS, though one whom I've yet to post anything substantial on) and, while I've come across a few references while looking back through this thread one was interested to note that he appears to gave rather vanished from History after the Election of 1948.
I would be very interested in reading your thoughts on what happened to him after he left the ... ummm, Executive Office ("Oval Office" seems inappropriate and the Powell House went to pieces even before the rest of Philadelphia was immolated); assuming he was of an age with his counterpart in Our Own History (Charles M La Follette was born 27 February 1898), he'd have been only 46 on leaving office (having presumably been the youngest Vice President since Breckinridge).
He might well have been slightly older (Robert La Follette's own sons were born in 1895 and 1897 respectively), but even so it seems very easy to imagine him attempting to mount a Political comeback (if only in pursuit of a little validation after being summarily rejected by the citizenry right after thrashing Jake Featherston like a dirty carpet and the Confederate States of America with him); one suspects he would have been #1 Challenger at the Socialist Convention of 1948 (assuming he was in a position comparable to that of Mr Gerald Ford in 1980) though somebody else clearly won the nomination in your timeline (making the parallels with President Ford even stronger!).
Another option I have seriously considered is that he might pull an Andrew Johnson and seek election to the United States Senate - he don't
need no stinking presidency! - then proceed from that lofty perch to make life more complicated for the Democrats for YEARS to come, very much in the fashion of old John Quincy Adams.
Your own opinion will almost certainly be different and I would be
especially interested in learning more if that were the case; half the fun of discussing Alternate History has always been seeing how things might have been very different, after all!