A big problem in getting a monorail in any big city in the US not associated with Disney is that, by your PoD, cars were king. The ALWEG proposal for LA, the only serious one in the 60s, was basically turned down in favor of nothing.
If you poo-poo AWOLAWOT, then there's pretty much no chance.
On the other hand, that one likely gives us as close as you're going to get to a system limited to the Capitol (or even the capital) - a monorail loop or line on the National Mall that's as much of a tourist attraction in and of itself as it is a transport system.