Why not? What would it be like then?
Well for one reason in the event of things 'going hot' Washington DC is going to be very near the top, if not at the top, of the list of targets to get hit with one or more nuclear weapons. Depending on how much build-up there has been will affect things such as whether the continuity of government evacuation plans have been readied, someone in the Presidential line of succession has been quietly stashed somewhere safe, whether members of the Congress are staying out of town etc. have happened or not. IIRC one of the incoming Presidents shortly after taking office decided to activate his emergency evacuation procedure as a test to see how it would cope, with the results being pretty shambolic and embarrassing for those concerned. Worst case scenario is that the missiles fly and a couple based on Cuba are able to destroy a large chunk of Washington DC and a large part of the government that gets caught. You would hope that they had things properly lined up and planned for, but this
is the government we're talking about so you can never be too sure.

At that point the there are so many ways things could go in various directions that politic developments would be almost unforeseeable.