Well after the two party system collapses after the 2016 elections:
A collapse like that would require an issue as deep and divisive as slavery in 1860. The central role of slavery was already established by the mid-1840's, so we should already be able to point to an equally deep issue today if it causes collapse by 2020. What issue today will still be there in 2020 and be deep enough to fracture both parties?
The War on Terror
The answer's a bit brief, but we can try to run with the ball anyway. I assume from the answer that the WOT has continued as a series of brushfire wars at various locations, but with a common thread of US-led interventions. To get to the map displayed, both the Democrats and Republicans need to split, then reform new coalitions, based on their direction to handle the WOT.
Which of the new parties emerge from which old parties, and what is their fundamental position on the WOT?