What would have happened if both unions had survived into the 20th century?

For starters, we would likely have the United States of America on the northern half and the Confederate States on the southern half as two different countries. There would likely be a lot of slaves attempting to cross the border from the south so that they could be free. Slavery would still be a thing in the south, of course. There is also a large chance that America would have gone to war with the southern states, although it would not be considered a civil war at this point. 

The re-election of the president abraham lincoln.