Do you realize that the Smithsonian is a series of museums that you cannot possibly see in a day? You could do 2 or maybe 3, just seeing the highlights.
Your days are quite light beyond this. I'm assuming you are just planning on walking by the Capitol and the White House or are you doing tours?
What time do you get there on the 14th? Will you have time to tour?
Heres what I would propose for an itinerary but its up to you.
American History Museum
Walk by of Capitol and White Houses (could cab it between or its a long walk)
Monument Tour (Recommend just doing this yourself, not a formal tour)
Arlington Cemetery (assuming good weather)
Holocaust Museum (get timed tickets for sometime in the afternoon NOW)
Portrait Gallery (is open much later than the rest of the museums)
Air & Space Museum
Will have time for more - check to see if DC has any special St Paddy's Day activities
Drive to NYC (or look at taking the train (Amtrak) rather than driving for a more relaxing method)