Your challenge today is one I find most challenging. I want you to have large numbers of German troops inside Washington DC. The only requirements are that the German troops be hostile and in large numbers. Also the US still has to exist.
This is a VERY low probability event, but could perhaps happen (or at least plausible for a good yarn/hollywood pic)
German POW's arrive in Baltimore for transfer to POW camps. Someone screws up badly, and they overpower the guards. Baltimore's also a port that a lot of stuff is shipped OUT of. Naturally, the POW's can't return home, or pull off a mass escape--but if they take DC, they can do some harm/bargain for release/whatever.
To really make things work well (from a drama standpoint, if not a realism standpoint) they manage not reveal who they are right away, and the train is dispatched by DC. They debark and move into the city--perhaps capturing FDR.
Like I said, low order probability bordering on ASB--but fits the bill.
CSA wins civil war, the politics happen and they end up allied with Germany (and maybe Britain). WWI begins and the CSA manages to hold on long enough for Germany to beat their enemies (whoever they may be) and start sending troops over to the CSA, slowly pushing the USA back until they attack Washington.
That's why Britain should be allies, so the Germans can have naval dominance and the US is fighting on two fronts.
The first thing that springs to mind is a large POW camp on the Mall.
Add one of John McClaine's ancestors and you'll see me at the movies every day