Washington has been eliminated from first place.

To show that Washington is eliminated from first place, we start with the current standings:
            Team	W	L	GL	PCT	GB
    Philadelphia	90	61	11	0.596	0.0
        New York	77	73	12	0.513	12.5
           Miami	70	80	12	0.467	19.5
         Atlanta	67	83	12	0.447	22.5
      Washington	62	88	12	0.413	27.5
           Total	366	385	59

Washington can finish the season with at most 62 + 12 = 74 wins and will finish the season behind the following teams:
Philadelphia has already won 90 games.
New York has already won 77 games.
# Washington Nationals' magic number
# Washington's magic number
# Nationals' magic number
# MLB Playoff Race