I don'I don't know. The midwest is very fragmented. Lots of teams to chose from. Since they're the most consistently successful they have more than their fair share. What I don't know is if St. Louis is a town where people grow up and stay in or come back to or if it's a place where people grow up, go to school and then move to one of the coasts. If that's the case, they'll have a pretty good fanbase nationally. Locally, it's as strong as any in baseball.
Friend of mine in Denver says the Rockies and are like the Cards in that they are a regional team, drawing from entire state or two. No reason the Nats can't do the same with Virginia. Huge population areas like Fredericksburg, Richmond, Hampton Roads, Roanoke, etc., can come up for the weekend or during the week when school is out.
I was in Norfolk this summer and a bar I visited had the Nats on in every TV in the place. Well, ok, there was one set tuned to the Boreoles.