According to Loverro the Nats are bidding to get the ASG in 2015 and the Os are in the running for 2016, since MLB won't likely award the game to the two cities in consecutive years it's likely an either/or situation with the loser waiting several more years.
I tend to lean more toward 2017 for the earliest possible Nats Park ASG - I recall reading somewhere (can't remember where exactly) that the Marlins had been all but promised the 2015 ASG if their new ground was finished on time, which it of course is. And 2019 may be a more realistic year since there could be carping from the Central and Western division clubs about the ASG going to an East club three consecutive times (Petco Park, for instance, hasn't gotten one yet, and neither has Great American Ballpark*; there also is some movement for Wrigley getting the 2014 ASG to celebrate its centennial, and oddly Dodger Stadium hasn't hosted it since 1980).
Baltimore last hosted the ASG in 1993, so they're about due - maybe as a consolation prize for Angelos if he is ultimately divested of the DC part of MASN?
*and they won't get it either as long as one Peter Edward Rose remains alive (or at least continues to be officially proscribed)