Only see I didn't know through in this is that Senate rules required a majority of all senators for the vice presidential vote, and not only that of those voting. Is that it ?
That was my understanding. The only example we have is in 1837, when the Senate voted to approve Vice Pres. Richard Johnson. That election had three abstentions, and yet the threshold remained 27 (out of 52 senators).
A contested election and potential US involvement in the Great War (aka World War I IOTL) earlier? Yeah, that's going to radicalize the populace considerably ITTL (just look at the Reds! timeline to see what can happen)...
The population is already quite a bit more radicalized than OTL 1912/13, but WWI certainly does have the potential to ramp that up.